Basic Math Examples

$(\frac{π}{π^{2}} + \frac{2}{2 - π} + \frac{1}{π + 2}) \div (π - 2 + \frac{10 - π^{2}}{π + 2})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{π}{π^{2}} + \frac{2}{2 - π} + \frac{1}{π + 2}}{π - 2 + \frac{10 - π^{2}}{π + 2}}$

Step 2

Cancel the common factor of $π$ and $π^{2}$ .

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Step 2.1

Multiply by $1$ .

$\frac{\frac{π \cdot 1}{π^{2}} + \frac{2}{2 - π} + \frac{1}{π + 2}}{π - 2 + \frac{10 - π^{2}}{π + 2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $π$ out of $π^{2}$ .

$\frac{\frac{π \cdot 1}{π π} + \frac{2}{2 - π} + \frac{1}{π + 2}}{π - 2 + \frac{10 - π^{2}}{π + 2}}$

Step 2.2.2

Cancel the common factor.

$\frac{\frac{π \cdot 1}{π π} + \frac{2}{2 - π} + \frac{1}{π + 2}}{π - 2 + \frac{10 - π^{2}}{π + 2}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{1}{π} + \frac{2}{2 - π} + \frac{1}{π + 2}}{π - 2 + \frac{10 - π^{2}}{π + 2}}$

Step 3

Multiply the numerator and denominator of the fraction by $π (2 - π) (π + 2)$ .

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Step 3.1

Multiply $\frac{\frac{1}{π} + \frac{2}{2 - π} + \frac{1}{π + 2}}{π - 2 + \frac{10 - π^{2}}{π + 2}}$ by $\frac{π (2 - π) (π + 2)}{π (2 - π) (π + 2)}$ .

$\frac{π (2 - π) (π + 2)}{π (2 - π) (π + 2)} \cdot \frac{\frac{1}{π} + \frac{2}{2 - π} + \frac{1}{π + 2}}{π - 2 + \frac{10 - π^{2}}{π + 2}}$

Step 3.2

Combine.

$\frac{π (2 - π) (π + 2) (\frac{1}{π} + \frac{2}{2 - π} + \frac{1}{π + 2})}{π (2 - π) (π + 2) (π - 2 + \frac{10 - π^{2}}{π + 2})}$

Step 4

Apply the distributive property.

$\frac{π (2 - π) (π + 2) \frac{1}{π} + π (2 - π) (π + 2) \frac{2}{2 - π} + π (2 - π) (π + 2) \frac{1}{π + 2}}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (π + 2) \frac{10 - π^{2}}{π + 2}}$

Step 5

Simplify by cancelling.

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Step 5.1

Cancel the common factor of $π$ .

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Step 5.1.1

Factor $π$ out of $π (2 - π) (π + 2)$ .

$\frac{π ((2 - π) (π + 2)) \frac{1}{π} + π (2 - π) (π + 2) \frac{2}{2 - π} + π (2 - π) (π + 2) \frac{1}{π + 2}}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (π + 2) \frac{10 - π^{2}}{π + 2}}$

Step 5.1.2

Cancel the common factor.

Step 5.1.3

Rewrite the expression.

$\frac{(2 - π) (π + 2) + π (2 - π) (π + 2) \frac{2}{2 - π} + π (2 - π) (π + 2) \frac{1}{π + 2}}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (π + 2) \frac{10 - π^{2}}{π + 2}}$

Step 5.2

Cancel the common factor of $2 - π$ .

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Step 5.2.1

Factor $2 - π$ out of $π (2 - π) (π + 2)$ .

$\frac{(2 - π) (π + 2) + (2 - π) (π (π + 2)) \frac{2}{2 - π} + π (2 - π) (π + 2) \frac{1}{π + 2}}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (π + 2) \frac{10 - π^{2}}{π + 2}}$

Step 5.2.2

Cancel the common factor.

Step 5.2.3

Rewrite the expression.

$\frac{(2 - π) (π + 2) + π (π + 2) \cdot 2 + π (2 - π) (π + 2) \frac{1}{π + 2}}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (π + 2) \frac{10 - π^{2}}{π + 2}}$

Step 5.3

Cancel the common factor of $π + 2$ .

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Step 5.3.1

Factor $π + 2$ out of $π (2 - π) (π + 2)$ .

$\frac{(2 - π) (π + 2) + π (π + 2) \cdot 2 + (π + 2) (π (2 - π)) \frac{1}{π + 2}}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (π + 2) \frac{10 - π^{2}}{π + 2}}$

Step 5.3.2

Cancel the common factor.

$\frac{(2 - π) (π + 2) + π (π + 2) \cdot 2 + (π + 2) (π (2 - π)) \frac{1}{π + 2}}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (π + 2) \frac{10 - π^{2}}{π + 2}}$

Step 5.3.3

Rewrite the expression.

$\frac{(2 - π) (π + 2) + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (π + 2) \frac{10 - π^{2}}{π + 2}}$

Step 5.4

Cancel the common factor of $π + 2$ .

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Step 5.4.1

Factor $π + 2$ out of $π (2 - π) (π + 2)$ .

$\frac{(2 - π) (π + 2) + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + (π + 2) (π (2 - π)) \frac{10 - π^{2}}{π + 2}}$

Step 5.4.2

Cancel the common factor.

$\frac{(2 - π) (π + 2) + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + (π + 2) (π (2 - π)) \frac{10 - π^{2}}{π + 2}}$

Step 5.4.3

Rewrite the expression.

$\frac{(2 - π) (π + 2) + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6

Simplify the numerator.

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Step 6.1

Expand $(2 - π) (π + 2)$ using the FOIL Method.

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Step 6.1.1

Apply the distributive property.

$\frac{2 (π + 2) - π (π + 2) + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.1.2

Apply the distributive property.

$\frac{2 π + 2 \cdot 2 - π (π + 2) + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.1.3

Apply the distributive property.

$\frac{2 π + 2 \cdot 2 - π π - π \cdot 2 + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.2

Simplify and combine like terms.

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Step 6.2.1

Simplify each term.

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Step 6.2.1.1

Multiply $2$ by $2$ .

$\frac{2 π + 4 - π π - π \cdot 2 + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.2.1.2

Multiply $- π π$ .

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Step 6.2.1.2.1

Raise $π$ to the power of $1$ .

$\frac{2 π + 4 - (π^{1} π) - π \cdot 2 + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.2.1.2.2

Raise $π$ to the power of $1$ .

$\frac{2 π + 4 - (π^{1} π^{1}) - π \cdot 2 + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.2.1.2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 π + 4 - π^{1 + 1} - π \cdot 2 + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.2.1.2.4

Add $1$ and $1$ .

$\frac{2 π + 4 - π^{2} - π \cdot 2 + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.2.1.3

Multiply $2$ by $- 1$ .

$\frac{2 π + 4 - π^{2} - 2 π + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.2.2

Subtract $2 π$ from $2 π$ .

$\frac{4 - π^{2} + 0 + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.2.3

Add $4$ and $0$ .

$\frac{- π^{2} + 4 + π (π + 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.3

Apply the distributive property.

$\frac{- π^{2} + 4 + (π π + π \cdot 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.4

Multiply $π π$ .

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Step 6.4.1

Raise $π$ to the power of $1$ .

$\frac{- π^{2} + 4 + (π^{1} π + π \cdot 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.4.2

Raise $π$ to the power of $1$ .

$\frac{- π^{2} + 4 + (π^{1} π^{1} + π \cdot 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- π^{2} + 4 + (π^{1 + 1} + π \cdot 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.4.4

Add $1$ and $1$ .

$\frac{- π^{2} + 4 + (π^{2} + π \cdot 2) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.5

Move $2$ to the left of $π$ .

$\frac{- π^{2} + 4 + (π^{2} + 2 \cdot π) \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.6

Apply the distributive property.

$\frac{- π^{2} + 4 + π^{2} \cdot 2 + 2 π \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.7

Move $2$ to the left of $π^{2}$ .

$\frac{- π^{2} + 4 + 2 \cdot π^{2} + 2 π \cdot 2 + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.8

Multiply $2$ by $2$ .

$\frac{- π^{2} + 4 + 2 \cdot π^{2} + 4 π + π (2 - π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.9

Apply the distributive property.

$\frac{- π^{2} + 4 + 2 π^{2} + 4 π + π \cdot 2 + π (- π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.10

Move $2$ to the left of $π$ .

$\frac{- π^{2} + 4 + 2 π^{2} + 4 π + 2 \cdot π + π (- π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.11

Multiply $π (- π)$ .

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Step 6.11.1

Raise $π$ to the power of $1$ .

$\frac{- π^{2} + 4 + 2 π^{2} + 4 π + 2 \cdot π - (π^{1} π)}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.11.2

Raise $π$ to the power of $1$ .

$\frac{- π^{2} + 4 + 2 π^{2} + 4 π + 2 \cdot π - (π^{1} π^{1})}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.11.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- π^{2} + 4 + 2 π^{2} + 4 π + 2 \cdot π - π^{1 + 1}}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.11.4

Add $1$ and $1$ .

$\frac{- π^{2} + 4 + 2 π^{2} + 4 π + 2 \cdot π - π^{2}}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.12

Add $- π^{2}$ and $2 π^{2}$ .

$\frac{π^{2} + 4 + 4 π + 2 π - π^{2}}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.13

Subtract $π^{2}$ from $π^{2}$ .

$\frac{4 + 4 π + 2 π + 0}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.14

Add $4 + 4 π + 2 π$ and $0$ .

$\frac{4 + 4 π + 2 π}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 6.15

Add $4 π$ and $2 π$ .

$\frac{4 + 6 π}{π (2 - π) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7

Simplify the denominator.

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Step 7.1

Apply the distributive property.

$\frac{4 + 6 π}{(π \cdot 2 + π (- π)) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.2

Move $2$ to the left of $π$ .

$\frac{4 + 6 π}{(2 \cdot π + π (- π)) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.3

Multiply $π (- π)$ .

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Step 7.3.1

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{(2 \cdot π - (π^{1} π)) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.3.2

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{(2 \cdot π - (π^{1} π^{1})) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 + 6 π}{(2 \cdot π - π^{1 + 1}) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.3.4

Add $1$ and $1$ .

$\frac{4 + 6 π}{(2 \cdot π - π^{2}) (π + 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.4

Expand $(2 π - π^{2}) (π + 2)$ using the FOIL Method.

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Step 7.4.1

Apply the distributive property.

$\frac{4 + 6 π}{(2 π (π + 2) - π^{2} (π + 2)) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.4.2

Apply the distributive property.

$\frac{4 + 6 π}{(2 π π + 2 π \cdot 2 - π^{2} (π + 2)) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.4.3

Apply the distributive property.

$\frac{4 + 6 π}{(2 π π + 2 π \cdot 2 - π^{2} π - π^{2} \cdot 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5

Simplify and combine like terms.

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Step 7.5.1

Simplify each term.

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Step 7.5.1.1

Multiply $2 π π$ .

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Step 7.5.1.1.1

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{(2 (π^{1} π) + 2 π \cdot 2 - π^{2} π - π^{2} \cdot 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5.1.1.2

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{(2 (π^{1} π^{1}) + 2 π \cdot 2 - π^{2} π - π^{2} \cdot 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5.1.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 + 6 π}{(2 π^{1 + 1} + 2 π \cdot 2 - π^{2} π - π^{2} \cdot 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5.1.1.4

Add $1$ and $1$ .

$\frac{4 + 6 π}{(2 π^{2} + 2 π \cdot 2 - π^{2} π - π^{2} \cdot 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5.1.2

Multiply $2$ by $2$ .

$\frac{4 + 6 π}{(2 π^{2} + 4 π - π^{2} π - π^{2} \cdot 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5.1.3

Multiply $π^{2}$ by $π$ by adding the exponents.

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Step 7.5.1.3.1

Move $π$ .

$\frac{4 + 6 π}{(2 π^{2} + 4 π - (π π^{2}) - π^{2} \cdot 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5.1.3.2

Multiply $π$ by $π^{2}$ .

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Step 7.5.1.3.2.1

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{(2 π^{2} + 4 π - (π^{1} π^{2}) - π^{2} \cdot 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5.1.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 + 6 π}{(2 π^{2} + 4 π - π^{1 + 2} - π^{2} \cdot 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5.1.3.3

Add $1$ and $2$ .

$\frac{4 + 6 π}{(2 π^{2} + 4 π - π^{3} - π^{2} \cdot 2) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5.1.4

Multiply $2$ by $- 1$ .

$\frac{4 + 6 π}{(2 π^{2} + 4 π - π^{3} - 2 π^{2}) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5.2

Subtract $2 π^{2}$ from $2 π^{2}$ .

$\frac{4 + 6 π}{(4 π - π^{3} + 0) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.5.3

Add $4 π$ and $0$ .

$\frac{4 + 6 π}{(- π^{3} + 4 π) π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.6

Apply the distributive property.

$\frac{4 + 6 π}{- π^{3} π + 4 π π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.7

Multiply $π^{3}$ by $π$ by adding the exponents.

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Step 7.7.1

Move $π$ .

$\frac{4 + 6 π}{- (π π^{3}) + 4 π π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.7.2

Multiply $π$ by $π^{3}$ .

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Step 7.7.2.1

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{- (π^{1} π^{3}) + 4 π π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.7.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 + 6 π}{- π^{1 + 3} + 4 π π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.7.3

Add $1$ and $3$ .

$\frac{4 + 6 π}{- π^{4} + 4 π π + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.8

Multiply $4 π π$ .

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Step 7.8.1

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 (π^{1} π) + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.8.2

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 (π^{1} π^{1}) + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.8.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 + 6 π}{- π^{4} + 4 π^{1 + 1} + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.8.4

Add $1$ and $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + π (2 - π) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.9

Apply the distributive property.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (π \cdot 2 + π (- π)) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.10

Move $2$ to the left of $π$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 \cdot π + π (- π)) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.11

Multiply $π (- π)$ .

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Step 7.11.1

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 \cdot π - (π^{1} π)) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.11.2

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 \cdot π - (π^{1} π^{1})) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.11.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 \cdot π - π^{1 + 1}) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.11.4

Add $1$ and $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 \cdot π - π^{2}) (π + 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.12

Expand $(2 π - π^{2}) (π + 2)$ using the FOIL Method.

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Step 7.12.1

Apply the distributive property.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 π (π + 2) - π^{2} (π + 2)) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.12.2

Apply the distributive property.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 π π + 2 π \cdot 2 - π^{2} (π + 2)) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.12.3

Apply the distributive property.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 π π + 2 π \cdot 2 - π^{2} π - π^{2} \cdot 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13

Simplify and combine like terms.

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Step 7.13.1

Simplify each term.

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Step 7.13.1.1

Multiply $2 π π$ .

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Step 7.13.1.1.1

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 (π^{1} π) + 2 π \cdot 2 - π^{2} π - π^{2} \cdot 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13.1.1.2

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 (π^{1} π^{1}) + 2 π \cdot 2 - π^{2} π - π^{2} \cdot 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13.1.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 π^{1 + 1} + 2 π \cdot 2 - π^{2} π - π^{2} \cdot 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13.1.1.4

Add $1$ and $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 π^{2} + 2 π \cdot 2 - π^{2} π - π^{2} \cdot 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13.1.2

Multiply $2$ by $2$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 π^{2} + 4 π - π^{2} π - π^{2} \cdot 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13.1.3

Multiply $π^{2}$ by $π$ by adding the exponents.

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Step 7.13.1.3.1

Move $π$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 π^{2} + 4 π - (π π^{2}) - π^{2} \cdot 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13.1.3.2

Multiply $π$ by $π^{2}$ .

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Step 7.13.1.3.2.1

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 π^{2} + 4 π - (π^{1} π^{2}) - π^{2} \cdot 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13.1.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 π^{2} + 4 π - π^{1 + 2} - π^{2} \cdot 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13.1.3.3

Add $1$ and $2$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 π^{2} + 4 π - π^{3} - π^{2} \cdot 2) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13.1.4

Multiply $2$ by $- 1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (2 π^{2} + 4 π - π^{3} - 2 π^{2}) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13.2

Subtract $2 π^{2}$ from $2 π^{2}$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (4 π - π^{3} + 0) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.13.3

Add $4 π$ and $0$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + (- π^{3} + 4 π) \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.14

Apply the distributive property.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} - π^{3} \cdot - 2 + 4 π \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.15

Multiply $- 2$ by $- 1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} + 4 π \cdot - 2 + π (2 - π) (10 - π^{2})}$

Step 7.16

Multiply $- 2$ by $4$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + π (2 - π) (10 - π^{2})}$

Step 7.17

Apply the distributive property.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + (π \cdot 2 + π (- π)) (10 - π^{2})}$

Step 7.18

Move $2$ to the left of $π$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + (2 \cdot π + π (- π)) (10 - π^{2})}$

Step 7.19

Multiply $π (- π)$ .

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Step 7.19.1

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + (2 \cdot π - (π^{1} π)) (10 - π^{2})}$

Step 7.19.2

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + (2 \cdot π - (π^{1} π^{1})) (10 - π^{2})}$

Step 7.19.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + (2 \cdot π - π^{1 + 1}) (10 - π^{2})}$

Step 7.19.4

Add $1$ and $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + (2 \cdot π - π^{2}) (10 - π^{2})}$

Step 7.20

Expand $(2 π - π^{2}) (10 - π^{2})$ using the FOIL Method.

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Step 7.20.1

Apply the distributive property.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 2 π (10 - π^{2}) - π^{2} (10 - π^{2})}$

Step 7.20.2

Apply the distributive property.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 2 π \cdot 10 + 2 π (- π^{2}) - π^{2} (10 - π^{2})}$

Step 7.20.3

Apply the distributive property.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 2 π \cdot 10 + 2 π (- π^{2}) - π^{2} \cdot 10 - π^{2} (- π^{2})}$

Step 7.21

Simplify each term.

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Step 7.21.1

Multiply $10$ by $2$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π + 2 π (- π^{2}) - π^{2} \cdot 10 - π^{2} (- π^{2})}$

Step 7.21.2

Multiply $π$ by $π^{2}$ by adding the exponents.

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Step 7.21.2.1

Move $π^{2}$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π + 2 (π^{2} π) \cdot - 1 - π^{2} \cdot 10 - π^{2} (- π^{2})}$

Step 7.21.2.2

Multiply $π^{2}$ by $π$ .

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Step 7.21.2.2.1

Raise $π$ to the power of $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π + 2 (π^{2} π^{1}) \cdot - 1 - π^{2} \cdot 10 - π^{2} (- π^{2})}$

Step 7.21.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π + 2 π^{2 + 1} \cdot - 1 - π^{2} \cdot 10 - π^{2} (- π^{2})}$

Step 7.21.2.3

Add $2$ and $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π + 2 π^{3} \cdot - 1 - π^{2} \cdot 10 - π^{2} (- π^{2})}$

Step 7.21.3

Multiply $- 1$ by $2$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π - 2 π^{3} - π^{2} \cdot 10 - π^{2} (- π^{2})}$

Step 7.21.4

Multiply $10$ by $- 1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π - 2 π^{3} - 10 π^{2} - π^{2} (- π^{2})}$

Step 7.21.5

Multiply $π^{2}$ by $π^{2}$ by adding the exponents.

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Step 7.21.5.1

Move $π^{2}$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π - 2 π^{3} - 10 π^{2} - (π^{2} π^{2}) \cdot - 1}$

Step 7.21.5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π - 2 π^{3} - 10 π^{2} - π^{2 + 2} \cdot - 1}$

Step 7.21.5.3

Add $2$ and $2$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π - 2 π^{3} - 10 π^{2} - π^{4} \cdot - 1}$

Step 7.21.6

Multiply $- π^{4} \cdot - 1$ .

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Step 7.21.6.1

Multiply $- 1$ by $- 1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π - 2 π^{3} - 10 π^{2} + 1 π^{4}}$

Step 7.21.6.2

Multiply $π^{4}$ by $1$ .

$\frac{4 + 6 π}{- π^{4} + 4 π^{2} + 2 π^{3} - 8 π + 20 π - 2 π^{3} - 10 π^{2} + π^{4}}$

Step 7.22

Add $- π^{4}$ and $π^{4}$ .

$\frac{4 + 6 π}{4 π^{2} + 2 π^{3} - 8 π + 20 π - 2 π^{3} - 10 π^{2} + 0}$

Step 7.23

Add $4 π^{2} + 2 π^{3} - 8 π + 20 π - 2 π^{3} - 10 π^{2}$ and $0$ .

$\frac{4 + 6 π}{4 π^{2} + 2 π^{3} - 8 π + 20 π - 2 π^{3} - 10 π^{2}}$

Step 7.24

Subtract $10 π^{2}$ from $4 π^{2}$ .

$\frac{4 + 6 π}{- 6 π^{2} + 2 π^{3} - 8 π + 20 π - 2 π^{3}}$

Step 7.25

Subtract $2 π^{3}$ from $2 π^{3}$ .

$\frac{4 + 6 π}{- 6 π^{2} + 0 - 8 π + 20 π}$

Step 7.26

Add $- 6 π^{2}$ and $0$ .

$\frac{4 + 6 π}{- 6 π^{2} - 8 π + 20 π}$

Step 7.27

Add $- 8 π$ and $20 π$ .

$\frac{4 + 6 π}{- 6 π^{2} + 12 π}$

Step 8

Simplify with factoring out.

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Step 8.1

Factor $- 1$ out of $- 6 π^{2}$ .

$\frac{4 + 6 π}{- (6 π^{2}) + 12 π}$

Step 8.2

Factor $- 1$ out of $12 π$ .

$\frac{4 + 6 π}{- (6 π^{2}) - (- 12 π)}$

Step 8.3

Factor $- 1$ out of $- (6 π^{2}) - (- 12 π)$ .

$\frac{4 + 6 π}{- (6 π^{2} - 12 π)}$

Step 8.4

Rewrite negatives.

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Step 8.4.1

Rewrite $- (6 π^{2} - 12 π)$ as $- 1 (6 π^{2} - 12 π)$ .

$\frac{4 + 6 π}{- 1 (6 π^{2} - 12 π)}$

Step 8.4.2

Move the negative in front of the fraction.

$- \frac{4 + 6 π}{6 π^{2} - 12 π}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{4 + 6 π}{6 π^{2} - 12 π}$

Decimal Form:

$- 1.06185563 \dots$