# How do you simplify (3x-2)/(x+3)+7/(x^2-x-12)?

Jul 2, 2017

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

#### Explanation:

First, factor out the denominator of the right hand term

$\frac{3 x - 2}{x + 3} + \frac{7}{\left(x + 3\right) \left(x - 4\right)}$

Next multiply the numerator and denominator of the first term by $\left(x - 4\right)$ in order to get a common denominator.

$\frac{x - 4}{x - 4} \frac{3 x - 2}{x + 3} + \frac{7}{\left(x + 3\right) \left(x - 4\right)}$

Combine the two fractions.

$\frac{\left(x - 4\right) \left(3 x - 2\right) + 7}{\left(x + 3\right) \left(x - 4\right)}$

Expand the numerator

$\frac{3 {x}^{2} - 12 x - 2 x + 8 + 7}{\left(x + 3\right) \left(x - 4\right)}$

Simplify the numerator

$\frac{3 {x}^{2} - 14 x + 15}{\left(x + 3\right) \left(x - 4\right)}$

Factor the numerator

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