Simplify (8/(x-4))÷((x^2+6x-16)/(x-2))

$\frac{8}{x - 4} \div \frac{x^{2} + 6 x - 16}{x - 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8}{x - 4} \cdot \frac{x - 2}{x^{2} + 6 x - 16}$

Step 2

Factor $x^{2} + 6 x - 16$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 16$ and whose sum is $6$ .

$- 2, 8$

Write the factored form using these integers.

$\frac{8}{x - 4} \cdot \frac{x - 2}{(x - 2) (x + 8)}$

Step 3

Simplify terms.

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\frac{8}{x - 4} \cdot \frac{x - 2}{(x - 2) (x + 8)}$

Rewrite the expression.

$\frac{8}{x - 4} \cdot \frac{1}{x + 8}$

Multiply $\frac{8}{x - 4}$ by $\frac{1}{x + 8}$ .

$\frac{8}{(x - 4) (x + 8)}$

Simplify (8/(x-4))÷((x^2+6x-16)/(x-2))

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