Question

The instructions say to solve by factoring, but I get stuck after I eliminate the denominator

Answer 1

30.
    5                3
-------- = 4 + --------
   x+4            x-2

    5              4 (x - 2) + 3
-------- = --------------------
    x+4              x - 2

    5              4x - 8 + 3
-------- = --------------------
    x+4              x - 2

   5              4x - 5
-------- = -------------
    x+4          x - 2

5(x-2) = (4x -5)(x+4)
5x - 10 = 4x^2  - 5x + 16x - 20
4x^2 + 6x - 10 = 0
2(2x^2 + 3x - 5) = 0
2(2x + 5)(x - 1) = 0
2x + 5 = 0; x = -5/2
x - 1 = 0; x = 1

answer
x = -5/2 and x = 1