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

Jun 4, 2018

x=$\frac{1}{3}$ or x=-2

#### Explanation:

Multiply $\frac{2 x}{x - 2}$ by x+1 so that the fractions are all over a common denominator

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

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

$\frac{3 {x}^{2} + 5 x}{\left(x + 1\right) \left(x - 2\right)} = \frac{2}{\left(x + 1\right) \left(x - 2\right)}$

mutiply throughout by (x+1)(x-2) to remove the fractions

$3 {x}^{2} + 5 x = 2$

$3 {x}^{2} + 5 x - 2 = 0$

(3x-1)(x+2)=0

3x-1=0 or x+2=0

x=$\frac{1}{3}$ or x=-2