Basic Math Examples

$\frac{π - 7}{3 π + 6} - \frac{4 π}{5 π - 3}$

Step 1

To write $\frac{π - 7}{3 π + 6}$ as a fraction with a common denominator, multiply by $\frac{5 π - 3}{5 π - 3}$ .

$\frac{π - 7}{3 π + 6} \cdot \frac{5 π - 3}{5 π - 3} - \frac{4 π}{5 π - 3}$

Step 2

To write $- \frac{4 π}{5 π - 3}$ as a fraction with a common denominator, multiply by $\frac{3 π + 6}{3 π + 6}$ .

$\frac{π - 7}{3 π + 6} \cdot \frac{5 π - 3}{5 π - 3} - \frac{4 π}{5 π - 3} \cdot \frac{3 π + 6}{3 π + 6}$

Step 3

Write each expression with a common denominator of $(3 π + 6) (5 π - 3)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{π - 7}{3 π + 6}$ by $\frac{5 π - 3}{5 π - 3}$ .

$\frac{(π - 7) (5 π - 3)}{(3 π + 6) (5 π - 3)} - \frac{4 π}{5 π - 3} \cdot \frac{3 π + 6}{3 π + 6}$

Step 3.2

Multiply $\frac{4 π}{5 π - 3}$ by $\frac{3 π + 6}{3 π + 6}$ .

$\frac{(π - 7) (5 π - 3)}{(3 π + 6) (5 π - 3)} - \frac{4 π (3 π + 6)}{(5 π - 3) (3 π + 6)}$

Step 3.3

Reorder the factors of $(5 π - 3) (3 π + 6)$ .

$\frac{(π - 7) (5 π - 3)}{(3 π + 6) (5 π - 3)} - \frac{4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 4

Combine the numerators over the common denominator.

$\frac{(π - 7) (5 π - 3) - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5

Simplify the numerator.

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Step 5.1

Expand $(π - 7) (5 π - 3)$ using the FOIL Method.

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Step 5.1.1

Apply the distributive property.

$\frac{π (5 π - 3) - 7 (5 π - 3) - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5.1.2

Apply the distributive property.

$\frac{π (5 π) + π \cdot - 3 - 7 (5 π - 3) - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5.1.3

Apply the distributive property.

$\frac{π (5 π) + π \cdot - 3 - 7 (5 π) - 7 \cdot - 3 - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5.2

Simplify and combine like terms.

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Multiply $π (5 π)$ .

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Step 5.2.1.1.1

Raise $π$ to the power of $1$ .

$\frac{5 (π^{1} π) + π \cdot - 3 - 7 (5 π) - 7 \cdot - 3 - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5.2.1.1.2

Raise $π$ to the power of $1$ .

$\frac{5 (π^{1} π^{1}) + π \cdot - 3 - 7 (5 π) - 7 \cdot - 3 - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5.2.1.1.3

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

$\frac{5 π^{1 + 1} + π \cdot - 3 - 7 (5 π) - 7 \cdot - 3 - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5.2.1.1.4

Add $1$ and $1$ .

$\frac{5 π^{2} + π \cdot - 3 - 7 (5 π) - 7 \cdot - 3 - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5.2.1.2

Move $- 3$ to the left of $π$ .

$\frac{5 π^{2} - 3 \cdot π - 7 (5 π) - 7 \cdot - 3 - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5.2.1.3

Multiply $5$ by $- 7$ .

$\frac{5 π^{2} - 3 π - 35 π - 7 \cdot - 3 - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5.2.1.4

Multiply $- 7$ by $- 3$ .

$\frac{5 π^{2} - 3 π - 35 π + 21 - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5.2.2

Subtract $35 π$ from $- 3 π$ .

$\frac{5 π^{2} - 38 π + 21 - 4 π (3 π + 6)}{(3 π + 6) (5 π - 3)}$

Step 5.3

Apply the distributive property.

$\frac{5 π^{2} - 38 π + 21 - 4 π (3 π) - 4 π \cdot 6}{(3 π + 6) (5 π - 3)}$

Step 5.4

Multiply $- 4 π (3 π)$ .

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Step 5.4.1

Multiply $3$ by $- 4$ .

$\frac{5 π^{2} - 38 π + 21 - 12 π π - 4 π \cdot 6}{(3 π + 6) (5 π - 3)}$

Step 5.4.2

Raise $π$ to the power of $1$ .

$\frac{5 π^{2} - 38 π + 21 - 12 (π^{1} π) - 4 π \cdot 6}{(3 π + 6) (5 π - 3)}$

Step 5.4.3

Raise $π$ to the power of $1$ .

$\frac{5 π^{2} - 38 π + 21 - 12 (π^{1} π^{1}) - 4 π \cdot 6}{(3 π + 6) (5 π - 3)}$

Step 5.4.4

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

$\frac{5 π^{2} - 38 π + 21 - 12 π^{1 + 1} - 4 π \cdot 6}{(3 π + 6) (5 π - 3)}$

Step 5.4.5

Add $1$ and $1$ .

$\frac{5 π^{2} - 38 π + 21 - 12 π^{2} - 4 π \cdot 6}{(3 π + 6) (5 π - 3)}$

Step 5.5

Multiply $6$ by $- 4$ .

$\frac{5 π^{2} - 38 π + 21 - 12 π^{2} - 24 π}{(3 π + 6) (5 π - 3)}$

Step 5.6

Subtract $12 π^{2}$ from $5 π^{2}$ .

$\frac{- 7 π^{2} - 38 π + 21 - 24 π}{(3 π + 6) (5 π - 3)}$

Step 5.7

Subtract $24 π$ from $- 38 π$ .

$\frac{- 7 π^{2} + 21 - 62 π}{(3 π + 6) (5 π - 3)}$

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- 7 π^{2}$ .

$\frac{- (7 π^{2}) + 21 - 62 π}{(3 π + 6) (5 π - 3)}$

Step 6.2

Rewrite $21$ as $- 1 (- 21)$ .

$\frac{- (7 π^{2}) - 1 (- 21) - 62 π}{(3 π + 6) (5 π - 3)}$

Step 6.3

Factor $- 1$ out of $- (7 π^{2}) - 1 (- 21)$ .

$\frac{- (7 π^{2} - 21) - 62 π}{(3 π + 6) (5 π - 3)}$

Step 6.4

Factor $- 1$ out of $- 62 π$ .

$\frac{- (7 π^{2} - 21) - (62 π)}{(3 π + 6) (5 π - 3)}$

Step 6.5

Factor $- 1$ out of $- (7 π^{2} - 21) - (62 π)$ .

$\frac{- (7 π^{2} - 21 + 62 π)}{(3 π + 6) (5 π - 3)}$

Step 6.6

Simplify the expression.

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Step 6.6.1

Rewrite $- (7 π^{2} - 21 + 62 π)$ as $- 1 (7 π^{2} - 21 + 62 π)$ .

$\frac{- 1 (7 π^{2} - 21 + 62 π)}{(3 π + 6) (5 π - 3)}$

Step 6.6.2

Move the negative in front of the fraction.

$- \frac{7 π^{2} - 21 + 62 π}{(3 π + 6) (5 π - 3)}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{7 π^{2} - 21 + 62 π}{(3 π + 6) (5 π - 3)}$

Decimal Form:

$- 1.23900141 \dots$