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

$\frac{2 {x}^{2} + 4 x + 12}{\left(x + 2\right) \left(x + 5\right)} \left(x + 2\right) = \frac{A}{x + 2} \cdot \left(x + 2\right) + \frac{B}{x + 5} \left(x + 2\right)$ 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
$\frac{2 {x}^{2} + 4 x + 12}{\left(x + 2\right) \left(x + 5\right)} = \frac{4}{x + 2} - \frac{14}{x + 5}$