# How do you simplify (x^2-x-12)/(x^2-11x+30)-(x-4)/(18-x)?

Feb 27, 2018

It can be factored into:
$\frac{\left(x - 4\right) \left(x + 3\right)}{\left(x - 6\right) \left(x - 5\right)} - \frac{x - 4}{18 - x}$

#### Explanation:

Starting with:
$\frac{{x}^{2} - x - 12}{{x}^{2} - 11 x + 30} - \frac{x - 4}{18 - x}$

It can be factored into:
$\frac{\left(x - 4\right) \left(x + 3\right)}{\left(x - 6\right) \left(x - 5\right)} - \frac{x - 4}{18 - x}$

I'm not sure how you are wanting this to simplify, but this should get you going. If this expression was equal to zero, you could add the second fraction to both sides and then divide by common factors (such as (x-4)).