# How do you combine (2p)/(p-5)-p/(p+6)?

May 24, 2018

$\frac{p \left(p + 17\right)}{\left(p - 5\right) \left(p + 6\right)}$

#### Explanation:

As explained below:

$\frac{2 p}{p - 5} - \frac{p}{p + 6}$

Treat this equation as normal fraction:

$\frac{2 p}{p - 5} - \frac{p}{p + 6}$

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

Open the brackets and we get:

$\frac{2 {p}^{2} + 12 p - {p}^{2} + 5 p}{\left(p - 5\right) \left(p + 6\right)}$

Re-arranging the like terms and we get:

$\frac{2 {p}^{2} - {p}^{2} + 12 p + 5 p}{\left(p - 5\right) \left(p + 6\right)}$

$\frac{{p}^{2} + 17 p}{\left(p - 5\right) \left(p + 6\right)}$

$\frac{p \left(p + 17\right)}{\left(p - 5\right) \left(p + 6\right)}$