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

May 11, 2018

color(blue)(x = 4, -3/2

#### Explanation:

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

$2 x \cdot \left(x - 1\right) = 3 \cdot \left(x + 4\right) , \text{ cross multiplying}$

$2 {x}^{2} - 2 x = 3 x + 12 , \text{ removing braces}$

$2 {x}^{2} - 2 x - 3 x - 12 = 0 , \text{ bringing all terms to L H S}$

$2 {x}^{2} - 5 x - 12 = 0 , \text{ simplifying}$

$2 {x}^{2} - 8 x + 3 x - 12 = 0$

$2 x \left(x - 4\right) + 3 \cdot \left(x - 4\right) = 0$

$\left(x - 4\right) \cdot \left(2 x + 3\right) = 0$

color(blue)(x = 4, -3/2