# How do you solve the rational equation  5 /( x+4) = 4 + 3/ (x-2)?

Jan 31, 2016

You must put everything on the same denominator and then solve the resulting quadratic equation.

#### Explanation:

The Least Common Denominator (LCM) would be (x + 4)(x - 2)

$\frac{5 \left(x - 2\right)}{\left(x + 4\right) \left(x - 2\right)}$ = $\frac{4 \left(x + 4\right) \left(x - 2\right)}{\left(x + 4\right) \left(x - 2\right)} + \frac{3 \left(x + 4\right)}{\left(x - 2\right) \left(x + 4\right)}$

5x - 10 = 4(${x}^{2}$ + 4x - 2x - 8) + 3x + 12

5x - 10 = $4 {x}^{2}$ + 8x - 32 + 3x + 12

0 = $4 {x}^{2}$ + 6x - 10

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

0 = 2($2 {x}^{2}$ + 5x - 2x - 5)

0 = 2(x(2x + 5) - (1(2x + 5))

0 = 2(x - 1)(2x + 5)

x = 1 and $- \frac{5}{2}$

Your solution set is x = 1 and $- \frac{5}{2}$