# How do you solve the rational equation (x+2)/(x+1)-(x-4)/(x-3)=0?

Jun 8, 2018

$x = 1$

#### Explanation:

add $\frac{x - 4}{x - 3}$ to both sides

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

multiply both sides by $\left(x + 1\right) \left(x - 3\right)$

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

${x}^{2} + 2 x - 3 x - 6 = {x}^{2} + x - 4 x - 4$

${x}^{2} - x - 6 = {x}^{2} - 3 x - 4$

add ${x}^{2}$ to both sides

$- x - 6 = - 3 x - 4$

add $3 x$ to both sides

$2 x - 6 = - 4$

add 6 to both sides

$2 x = 2$

divide by 2

$x = 1$