Simplify (x^2+2x-8)/((x-2)(x+6))

$\frac{x^{2} + 2 x - 8}{(x - 2) (x + 6)}$

Step 1

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 $2$ .

$- 2, 4$

Write the factored form using these integers.

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

Step 2

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (x^2+2x-8)/((x-2)(x+6))

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