# How do you simplify (2x)/(x^2+8x+15)-(x+3)/(x+5)?

Jul 6, 2017

$\frac{{x}^{2} + 8 x + 9}{{x}^{2} + 8 x + 15}$

#### Explanation:

To simplify this one must first find the common denominator. This is found by first factoring ${x}^{2} + 8 x + 15$.
This factors into $\left(x + 5\right) \left(x + 3\right)$

Next multiply the 2nd fraction by $\frac{x + 3}{x + 3}$ to make the denominators equal.

$\frac{2 x}{{x}^{2} + 8 x + 15} - \frac{x + 3}{x + 5} \cdot \frac{x + 3}{x + 3}$

$\frac{2 x}{{x}^{2} + 8 x + 15} - \frac{\left(x + 3\right) \left(x + 3\right)}{\left(x + 3\right) \left(x + 5\right)}$

$\left(x + 3\right) \left(x + 3\right) = {x}^{2} + 6 x + 9$, so combining these,

$\frac{2 x}{{x}^{2} + 8 x + 15} - \frac{{x}^{2} + 6 x + 9}{{x}^{2} + 8 x + 15} = \frac{{x}^{2} + 8 x + 9}{{x}^{2} + 8 x + 15}$