Simplify ((a-4)/(a^2-2a-8))÷(1/(a-5))

$\frac{a - 4}{a^{2} - 2 a - 8} \div \frac{1}{a - 5}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{a - 4}{a^{2} - 2 a - 8} (a - 5)$

Step 2

Factor $a^{2} - 2 a - 8$ 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 $- 8$ and whose sum is $- 2$ .

$- 4, 2$

Write the factored form using these integers.

$\frac{a - 4}{(a - 4) (a + 2)} (a - 5)$

Step 3

Simplify terms.

Cancel the common factor of $a - 4$ .

Cancel the common factor.

$\frac{a - 4}{(a - 4) (a + 2)} (a - 5)$

Rewrite the expression.

$\frac{1}{a + 2} (a - 5)$

Multiply $\frac{1}{a + 2}$ by $a - 5$ .

$\frac{a - 5}{a + 2}$

Simplify ((a-4)/(a^2-2a-8))÷(1/(a-5))

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