Simplify (8x-16)/(x^2-13x+22)

$\frac{8 x - 16}{x^{2} - 13 x + 22}$

Step 1

Factor $8$ out of $8 x - 16$ .

Factor $8$ out of $8 x$ .

$\frac{8 (x) - 16}{x^{2} - 13 x + 22}$

Factor $8$ out of $- 16$ .

$\frac{8 x + 8 \cdot - 2}{x^{2} - 13 x + 22}$

Factor $8$ out of $8 x + 8 \cdot - 2$ .

$\frac{8 (x - 2)}{x^{2} - 13 x + 22}$

Step 2

Factor $x^{2} - 13 x + 22$ 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 $22$ and whose sum is $- 13$ .

$- 11, - 2$

Write the factored form using these integers.

$\frac{8 (x - 2)}{(x - 11) (x - 2)}$

Step 3

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\frac{8 (x - 2)}{(x - 11) (x - 2)}$

Rewrite the expression.

$\frac{8}{x - 11}$

Simplify (8x-16)/(x^2-13x+22)

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