# How do you express (2x^2+4x+12)/(x^2+7x+10) in partial fractions?

##### 1 Answer
Mar 1, 2016

$\frac{2 {x}^{2} + 4 x + 12}{\left(x + 2\right) \left(x + 5\right)} \left(x + 2\right) = \frac{A}{x + 2} \cdot \left(x + 2\right) + \frac{B}{x + 5} \left(x + 2\right)$ Simplify and put in -2 for x, $A = 4$
$\frac{2 {x}^{2} + 4 x + 12}{\left(x + 2\right) \left(x + 5\right)} \left(x + 5\right) = \frac{A}{x + 2} \left(x + 5\right) + \frac{B}{x + 5} \left(x + 5\right)$ Simplify and put in -5 for x, B= -14
$\frac{2 {x}^{2} + 4 x + 12}{\left(x + 2\right) \left(x + 5\right)} = \frac{4}{x + 2} - \frac{14}{x + 5}$

#### Explanation:

To resolve into partial fractions, factor the denominator and split it into fractions. Note that A and B stands for constants. Once you split it up then multiply everything on both sides by x+2, simplify, then put in -2 for x to zero out the other fraction so we can solve for A. Do the same thing for B. Multiply everything on both sides by x+5 and put in -5 to zero out the A so we can solve for B. Once you find the values for A and B then put it into the partial fractions at the beginning.