# How do you solve 2/(x+1) + 5/(x-2)=-2?

Oct 29, 2017

Solution: $x = \frac{1}{2} \mathmr{and} x = - 3$

#### Explanation:

$\frac{2}{x + 1} + \frac{5}{x - 2} = - 2$ . Multiplying by $\left(x + 1\right) \left(x - 2\right)$ on both

sides we get , $2 \left(x - 2\right) + 5 \left(x + 1\right) = - 2 \left(x + 1\right) \left(x - 2\right)$ or

$2 x - 4 + 5 x + 5 = - 2 \left({x}^{2} - x - 2\right)$or

$7 x + 1 = - 2 {x}^{2} + 2 x + 4 \mathmr{and} 2 {x}^{2} + 5 x - 3 = 0$ or

$2 {x}^{2} + 6 x - x - 3 = 0 \mathmr{and} 2 x \left(x + 3\right) - 1 \left(x + 3\right) = 0$ or

$\left(x + 3\right) \left(2 x - 1\right) = 0$. Either $x + 3 = 0 \therefore x = - 3$ or

$2 x - 1 = 0 \therefore x = \frac{1}{2}$

Solution: $x = \frac{1}{2} \mathmr{and} x = - 3$ [Ans]