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

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.