Simplify (x^2-11x+18)/(x^2+2x-8)

$\frac{x^{2} - 11 x + 18}{x^{2} + 2 x - 8}$

Step 1

Factor $x^{2} - 11 x + 18$ 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 $18$ and whose sum is $- 11$ .

$- 9, - 2$

Write the factored form using these integers.

$\frac{(x - 9) (x - 2)}{x^{2} + 2 x - 8}$

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 $2$ .

$- 2, 4$

Write the factored form using these integers.

$\frac{(x - 9) (x - 2)}{(x - 2) (x + 4)}$

Step 3

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\frac{(x - 9) (x - 2)}{(x - 2) (x + 4)}$

Rewrite the expression.

$\frac{x - 9}{x + 4}$

Simplify (x^2-11x+18)/(x^2+2x-8)

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