# How do you simplify (8x-16)/(x^2-13x+22) and find the restrictions on the variable?

Feb 11, 2018

8/(x-11);x cannot be $11$

#### Explanation:

$- 11 - 2 = - 13$

$- 11 \cdot - 2 = 22$

${x}^{2} - 13 x + 22 = \left(x - 11\right) \left(x - 2\right)$

$8 x - 16 = 8 \left(x - 2\right)$

$\frac{8 x - 16}{{x}^{2} - 13 x + 22} = \frac{8 \left(x - 2\right)}{\left(x - 11\right) \left(x - 2\right)}$

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

$\frac{n}{0} =$ undefined

the denominator, $x - 11$, cannot be $0$.

this means that $x$ cannot be $11$.

graph{8/(x-11) [-17.88, 38.62, -19.63, 9.8]}