# How do you solve 4 / (x+1) + 3 / (x - 4) = 2 / (x +1)?

Oct 3, 2016

$x = 1$

#### Explanation:

The usual approach might be to multiply by the LCD to cancel the denominators. However two of the denominators are the same.
Put them together on one side.

$\frac{4}{x + 1} + \frac{3}{x - 4} = \frac{2}{x + 1}$

$\textcolor{red}{\frac{4}{x + 1} - \frac{2}{x + 1}} = - \frac{3}{x - 4}$

$\frac{2}{x + 1} = \frac{3}{-} \left(x - 4\right) \text{ } \leftarrow$ one fraction each side, cross-multiply

$3 \left(x + 1\right) = - 2 \left(x - 4\right)$

$3 x + 3 = - 2 x + 8$

$3 x + 2 x = 8 - 3$

$5 x = 5$

$x = 1$