# How do you combine (5x-1)/((2x+9)(x-6))-(3x-6)/((2x+9)(x-6))?

Apr 2, 2017

$\frac{2 x + 5}{\left(2 x + 9\right) \left(x - 6\right)}$

#### Explanation:

Since both have the same denominator you can directly add/subtract the numerators:

$\frac{\left(5 x - 1\right) - \left(3 x - 6\right)}{\left(2 x + 9\right) \left(x - 6\right)}$

Make sure to distribute the negative correctly:
$\frac{5 x - 1 - 3 x + 6}{\left(2 x + 9\right) \left(x - 6\right)} = \frac{\left(5 x - 3 x\right) + \left(- 1 + 6\right)}{\left(2 x + 9\right) \left(x - 6\right)}$

$= \frac{2 x + 5}{\left(2 x + 9\right) \left(x - 6\right)}$