# How can I change f(x) = (2x-1)/(x+2) into the form A + B/(x+2) where A and B are both integers?

Aug 20, 2017

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

#### Explanation:

$\text{using "(x+2)" as a factor in the numerator}$

$\text{consider the numerator}$

$2 \left(x + 2\right) \textcolor{m a \ge n t a}{- 4} - 1$

$= 2 \left(x + 2\right) - 5$

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

$\textcolor{b l u e}{\text{As a check}}$

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

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

$= \frac{2 x + 4 - 5}{x + 2} = \frac{2 x - 1}{x + 2} \leftarrow \text{ True}$