# How do you simplify (x-5)div(x^2-11x+30)/(x^2+7x+12)*(x-6)?

Jun 28, 2017

This can be simplified to $\left(x + 4\right) \left(x + 3\right)$.

#### Explanation:

Start by transforming the division into a multiplication.

$= \left(x - 5\right) \cdot \frac{{x}^{2} + 7 x + 12}{{x}^{2} - 11 x + 30} \cdot \left(x - 6\right)$

$= \frac{\left(x - 5\right) \left(x + 4\right) \left(x + 3\right) \left(x - 6\right)}{\left(x - 5\right) \left(x - 6\right)}$

$= \left(x + 4\right) \left(x + 3\right)$

It's also worth noting that $x \ne - 4 , - 3 , 5 \mathmr{and} 6$

Hopefully this helps!