Basic Math Examples

$\frac{π^{2} - q^{2}}{π - q} \div \frac{π}{π^{2} - q π}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{π^{2} - q^{2}}{π - q} \cdot \frac{π^{2} - q π}{π}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = π$ and $b = q$ .

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $π - q$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Divide $π + q$ by $1$ .

$(π + q) \frac{π^{2} - q π}{π}$

Step 3.2

Apply the distributive property.

$π \frac{π^{2} - q π}{π} + q \frac{π^{2} - q π}{π}$

Step 3.3

Cancel the common factor of $π$ .

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Step 3.3.1

Cancel the common factor.

$π \frac{π^{2} - q π}{π} + q \frac{π^{2} - q π}{π}$

Step 3.3.2

Rewrite the expression.

$π^{2} - q π + q \frac{π^{2} - q π}{π}$

Step 3.4

Combine $q$ and $\frac{π^{2} - q π}{π}$ .

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

Step 4

Find the common denominator.

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Step 4.1

Write $π^{2}$ as a fraction with denominator $1$ .

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

Step 4.2

Multiply $\frac{π^{2}}{1}$ by $\frac{π}{π}$ .

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

Step 4.3

Multiply $\frac{π^{2}}{1}$ by $\frac{π}{π}$ .

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

Step 4.4

Write $- q π$ as a fraction with denominator $1$ .

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

Step 4.5

Multiply $\frac{- q π}{1}$ by $\frac{π}{π}$ .

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

Step 4.6

Multiply $\frac{- q π}{1}$ by $\frac{π}{π}$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify each term.

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Step 6.1

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

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Step 6.1.1

Multiply $π^{2}$ by $π$ .

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Step 6.1.1.1

Raise $π$ to the power of $1$ .

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

Step 6.1.1.2

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

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

Step 6.1.2

Add $2$ and $1$ .

$\frac{π^{3} - q π π + q (π^{2} - q π)}{π}$

Step 6.2

Multiply $- q π π$ .

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Step 6.2.1

Raise $π$ to the power of $1$ .

$\frac{π^{3} - q (π^{1} π) + q (π^{2} - q π)}{π}$

Step 6.2.2

Raise $π$ to the power of $1$ .

$\frac{π^{3} - q (π^{1} π^{1}) + q (π^{2} - q π)}{π}$

Step 6.2.3

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

$\frac{π^{3} - q π^{1 + 1} + q (π^{2} - q π)}{π}$

Step 6.2.4

Add $1$ and $1$ .

$\frac{π^{3} - q π^{2} + q (π^{2} - q π)}{π}$

Step 6.3

Apply the distributive property.

$\frac{π^{3} - q π^{2} + q π^{2} + q (- q π)}{π}$

Step 6.4

Rewrite using the commutative property of multiplication.

$\frac{π^{3} - q π^{2} + q π^{2} - π q \cdot q}{π}$

Step 6.5

Multiply $q$ by $q$ by adding the exponents.

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Step 6.5.1

Move $q$ .

$\frac{π^{3} - q π^{2} + q π^{2} - π (q \cdot q)}{π}$

Step 6.5.2

Multiply $q$ by $q$ .

$\frac{π^{3} - q π^{2} + q π^{2} - π q^{2}}{π}$

Step 7

Combine the opposite terms in $π^{3} - q π^{2} + q π^{2} - π q^{2}$ .

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Step 7.1

Add $- q π^{2}$ and $q π^{2}$ .

$\frac{π^{3} + 0 - π q^{2}}{π}$

Step 7.2

Add $π^{3}$ and $0$ .

$\frac{π^{3} - π q^{2}}{π}$