# How do you subtract \frac { x ^ { 2} - 10x } { x ^ { 2} - 11x - 12} - \frac { 24} { x ^ { 2} - 11x - 12}?

Jun 7, 2017

It's $\frac{x + 2}{x + 1}$.

#### Explanation:

$\frac{{x}^{2} - 10 x}{{x}^{2} - 11 x - 12} - \frac{24}{{x}^{2} - 11 x - 12}$

Noting that the two fractions have common denominators, we can simplify the expression as so:

$\frac{{x}^{2} - 10 x - 24}{{x}^{2} - 11 x - 12}$

Then, we can factor both the numerator and the denominator into a $\left(x + a\right) \left(x + b\right)$ format:

$\frac{\left(x + 2\right) \left(x - 12\right)}{\left(x + 1\right) \left(x - 12\right)}$

Then, we cancel the $x - 12$s and finish the problem with the final answer:

$\frac{x + 2}{x + 1}$