Cancel the Common Factors (5x-20)/(x^2-2x-8)

$\frac{5 x - 20}{x^{2} - 2 x - 8}$

Step 1

Factor $5$ out of $5 x - 20$ .

Factor $5$ out of $5 x$ .

$\frac{5 (x) - 20}{x^{2} - 2 x - 8}$

Factor $5$ out of $- 20$ .

$\frac{5 x + 5 \cdot - 4}{x^{2} - 2 x - 8}$

Factor $5$ out of $5 x + 5 \cdot - 4$ .

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

Step 2

Factor $x^{2} - 2 x - 8$ 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.

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

Step 3

Reduce the expression $\frac{5 (x - 4)}{(x - 4) (x + 2)}$ by cancelling the common factors.

Cancel the common factor.

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

Rewrite the expression.

$\frac{5}{x + 2}$

Cancel the Common Factors (5x-20)/(x^2-2x-8)

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