Question

Solve the rational equation 1/(x-2)-1/(x+3) = 1/5

Answer 1

x = 5.09, -6.09.

Explanation:

1/(x-2) - 1/(x+3) = 1/5

Multiply through by the LCM 5(x-2)(x+3):

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

5x + 15 - 5x + 10 = x^2 + x - 6

x^2 + x - 31 = 0

x = [ -1 +/- sqrt(1 - 1*1*31)] / 2

x = 5.09, -6.09.