Answer:
x = 5.09, -6.09.
Step-by-step 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.
