# How do you simplify (x+3)/(x+5) + 6/(x^2+3x-10)?

Apr 9, 2018

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

#### Explanation:

The quadratic can be factored to $\left(x + 5\right) \left(x - 2\right)$.

So the expression is:
$\frac{x + 3}{x + 5} + \frac{6}{\left(x - 2\right) \left(x + 5\right)}$

Obtain a common denominator:
$\frac{x + 3}{x + 5} \cdot \frac{x - 2}{x - 2}$ --> $\frac{\left(x + 3\right) \left(x - 2\right)}{\left(x + 5\right) \left(x - 2\right)}$

So the expression is now:
$\frac{6 + \left(x + 3\right) \left(x - 2\right)}{\left(x + 5\right) \left(x - 2\right)}$
$\frac{6 + {x}^{2} + x - 6}{\left(x + 5\right) \left(x - 2\right)}$

Sixes cancel, top factor out an x:
$\frac{x \left(x + 1\right)}{\left(x + 5\right) \left(x - 2\right)}$

And that is it. Make sure you state that x cannot be $- 5$ or $2$, since that would result in division by zero.