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

May 29, 2016

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

#### Explanation:

$\frac{{x}^{2} + 2}{x + 2}$

$= \frac{{x}^{2} + 2 x - 2 x - 4 + 6}{x + 2}$

$= \frac{x \left(x + 2\right) - 2 \left(x + 2\right) + 6}{x + 2}$

$= x - 2 + \frac{6}{x + 2}$

If you prefer, you can long divide the coefficients like this:

Notice the $0$ in the dividend to stand for the missing $x$ term in the numerator.