Simplify (6x-24)/(16-x^2)

$\frac{6 x - 24}{16 - x^{2}}$

Factor $6$ out of $6 x - 24$ .

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Factor $6$ out of $6 x$ .

$\frac{6 (x) - 24}{16 - x^{2}}$

Factor $6$ out of $- 24$ .

$\frac{6 x + 6 \cdot - 4}{16 - x^{2}}$

Factor $6$ out of $6 x + 6 \cdot - 4$ .

$\frac{6 (x - 4)}{16 - x^{2}}$

Simplify the denominator.

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

$\frac{6 (x - 4)}{4^{2} - x^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4$ and $b = x$ .

$\frac{6 (x - 4)}{(4 + x) (4 - x)}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor of $x - 4$ and $4 - x$ .

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Factor $- 1$ out of $x$ .

$\frac{6 (- 1 (- x) - 4)}{(4 + x) (4 - x)}$

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{6 (- 1 (- x) - 1 (4))}{(4 + x) (4 - x)}$

Factor $- 1$ out of $- 1 (- x) - 1 (4)$ .

$\frac{6 (- 1 (- x + 4))}{(4 + x) (4 - x)}$

Reorder terms.

$\frac{6 \cdot - 1 (- x + 4)}{(4 + x) (- x + 4)}$

Cancel the common factor.

$\frac{6 \cdot - 1 (- x + 4)}{(4 + x) (- x + 4)}$

Rewrite the expression.

$\frac{6 \cdot - 1}{4 + x}$

Simplify the expression.

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Multiply $6$ by $- 1$ .

$\frac{- 6}{4 + x}$

Move the negative in front of the fraction.

$- \frac{6}{4 + x}$

Simplify (6x-24)/(16-x^2)

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