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

Mar 22, 2018

$x$ = $1$.

#### Explanation:

First, multiply and divide the first fraction on the left by $x - 4$ and the second fraction on the left by $x + 1$ to make them comparable.

We get $\frac{4 \left(x - 4\right) + 3 \left(x + 1\right)}{\left(x + 1\right) \left(x - 4\right)}$ = $\frac{2}{x + 1}$.

After cancelling $x + 1$ on both sides, we get,

$\frac{4 \left(x - 4\right) + 3 \left(x + 1\right)}{x - 4}$ = $2$.

On expanding the numerator and cross multiplying the denominator we get,

$7 x - 13$ = $2 x - 8$

This gives us $5 x$ = $5$

And thus $x$ = $1$.