Pre-Algebra Examples

$\frac{m^{2} - 64}{m + 9} \div \frac{8 - m}{m}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{m^{2} - 64}{m + 9} \cdot \frac{m}{8 - m}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $64$ as $8^{2}$ .

$\frac{m^{2} - 8^{2}}{m + 9} \cdot \frac{m}{8 - m}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = 8$ .

$\frac{(m + 8) (m - 8)}{m + 9} \cdot \frac{m}{8 - m}$

Step 3

Multiply $\frac{(m + 8) (m - 8)}{m + 9}$ by $\frac{m}{8 - m}$ .

$\frac{(m + 8) (m - 8) m}{(m + 9) (8 - m)}$

Step 4

Cancel the common factor of $m - 8$ and $8 - m$ .

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Step 4.1

Factor $- 1$ out of $m$ .

$\frac{(m + 8) (- 1 (- m) - 8) m}{(m + 9) (8 - m)}$

Step 4.2

Rewrite $- 8$ as $- 1 (8)$ .

$\frac{(m + 8) (- 1 (- m) - 1 (8)) m}{(m + 9) (8 - m)}$

Step 4.3

Factor $- 1$ out of $- 1 (- m) - 1 (8)$ .

$\frac{(m + 8) (- 1 (- m + 8)) m}{(m + 9) (8 - m)}$

Step 4.4

Reorder terms.

$\frac{(m + 8) (- 1 (- m + 8)) m}{(m + 9) (- m + 8)}$

Step 4.5

Cancel the common factor.

$\frac{(m + 8) (- 1 (- m + 8)) m}{(m + 9) (- m + 8)}$

Step 4.6

Rewrite the expression.

$\frac{((m + 8) \cdot (- 1)) m}{m + 9}$

Step 5

Factor out negative.

$\frac{- (m + 8) m}{m + 9}$

Step 6

Move the negative in front of the fraction.

$- \frac{(m + 8) m}{m + 9}$

Step 7

Reorder factors in $- \frac{(m + 8) m}{m + 9}$ .

$- \frac{m (m + 8)}{m + 9}$