# How do you combine 2/(3x-15)+x/(25-x^2)?

Feb 9, 2017

$\frac{2}{3 x - 15} + \frac{x}{25 - {x}^{2}} = \frac{10 - x}{3 {x}^{2} - 75}$

#### Explanation:

$\frac{2}{3 x - 15} + \frac{x}{25 - {x}^{2}}$

= $\frac{2}{3 \left(x - 5\right)} - \frac{x}{{x}^{2} - 25}$ - we have modified so that both may have common factor $\left(x - 5\right)$

= $\frac{2}{3 \left(x - 5\right)} - \frac{x}{{x}^{2} - {5}^{2}}$

= $\frac{2}{3 \left(x - 5\right)} - \frac{x}{\left(x - 5\right) \left(x + 5\right)}$

= $\frac{2 \left(x + 5\right) - 3 x}{3 \left(x - 5\right) \left(x + 5\right)}$

= $\frac{2 x + 10 - 3 x}{3 \left(x - 5\right) \left(x + 5\right)}$

= $\frac{10 - x}{3 \left(x - 5\right) \left(x + 5\right)}$

= $\frac{10 - x}{3 \left({x}^{2} - 25\right)}$

= $\frac{10 - x}{3 {x}^{2} - 75}$