Algebra Examples

$\frac{\frac{m + 3}{m^{2} - 16}}{\frac{m^{2 - 9}}{m + 4}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{m + 3}{m^{2} - 16} \cdot \frac{m + 4}{m^{2 - 9}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$\frac{m + 3}{m^{2} - 4^{2}} \cdot \frac{m + 4}{m^{2 - 9}}$

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 $b = 4$ .

$\frac{m + 3}{(m + 4) (m - 4)} \cdot \frac{m + 4}{m^{2 - 9}}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $m + 4$ .

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Step 3.1.1

Cancel the common factor.

$\frac{m + 3}{(m + 4) (m - 4)} \cdot \frac{m + 4}{m^{2 - 9}}$

Step 3.1.2

Rewrite the expression.

$\frac{m + 3}{m - 4} \cdot \frac{1}{m^{2 - 9}}$

Step 3.2

Multiply $\frac{m + 3}{m - 4}$ by $\frac{1}{m^{2 - 9}}$ .

$\frac{m + 3}{(m - 4) m^{2 - 9}}$

Step 3.3

Move $m^{2 - 9}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{(m + 3) m^{- (2 - 9)}}{m - 4}$

Step 4

Simplify the numerator.

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Step 4.1

Subtract $9$ from $2$ .

$\frac{(m + 3) m^{- - 7}}{m - 4}$

Step 4.2

Multiply $- 1$ by $- 7$ .

$\frac{(m + 3) m^{7}}{m - 4}$

Step 5

Reorder factors in $\frac{(m + 3) m^{7}}{m - 4}$ .

$\frac{m^{7} (m + 3)}{m - 4}$