Question

Solve
3/ x-2 - 2/ x+3 =1
Leave your answer in surd form.

Answer 1

Explanation:

3/(x-2) - 2/(x+3) = 1....multiply everything by (x-2)(x+3)

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

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

3x + 9 -2x + 4 = (x-2)(x+3)

x + 13 = x^2 + x - 6

x^2 - x + x - 6 - 13 = 0

x^2 - 19 = 0

x^2 = 19....take sq rt of both sides

sqrt(x^2) = sqrt 19

x = sqrt 19 and x = - sqrt 19 <====