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

Jul 13, 2016

The Soln. $: x = 1$

Explanation:

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

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

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

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

$\therefore 2 x - 8 = - 3 x - 3$

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

$\therefore 5 x = 5$

$\therefore x = 1$

Hence, the Soln. $: x = 1$