# How do you combine (x^2+13x+18)/(x^2-9)+(x+1)/(x+3)?

Jul 24, 2016

$\frac{2 {x}^{2} + 11 x + 15}{\left(x + 3\right) \left(x - 3\right)}$

#### Explanation:

$\frac{{x}^{2} + 13 x + 18}{{x}^{2} - 9} + \frac{x + 1}{x + 3}$
$= \frac{{x}^{2} + 13 x + 18}{\left(x + 3\right) \left(x - 3\right)} + \frac{x + 1}{x + 3}$
$= \frac{{x}^{2} + 13 x + 18 + \left(x + 1\right) \left(x - 3\right)}{\left(x + 3\right) \left(x - 3\right)}$
$= \frac{{x}^{2} + 13 x + 18 + {x}^{2} - 3 x + x - 3}{\left(x + 3\right) \left(x - 3\right)}$
$\frac{2 {x}^{2} + 11 x + 15}{\left(x + 3\right) \left(x - 3\right)}$

Jul 24, 2016

$\frac{{x}^{2} + 13 x + 18}{{x}^{2} - 9} + \frac{x + 1}{x + 3} = \frac{2 x + 5}{x - 3}$

#### Explanation:

$\frac{{x}^{2} + 13 x + 18}{{x}^{2} - 9} + \frac{x + 1}{x + 3}$

= $\frac{{x}^{2} + 13 x + 18}{\left(x + 3\right) \left(x - 3\right)} + \frac{x + 1}{x + 3}$

= $\frac{{x}^{2} + 13 x + 18 + \left(x + 1\right) \left(x - 3\right)}{\left(x + 3\right) \left(x - 3\right)}$

= $\frac{{x}^{2} + 13 x + 18 + \left({x}^{2} - 3 x + x - 3\right)}{\left(x + 3\right) \left(x - 3\right)}$

= $\frac{2 {x}^{2} + 11 x + 15}{\left(x + 3\right) \left(x - 3\right)}$

= $\frac{2 {x}^{2} + 5 x + 6 x + 15}{\left(x + 3\right) \left(x - 3\right)}$

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

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

= $\frac{2 x + 5}{x - 3}$