Can someone please break down how to solve this equation. I am so confused.

Question

(x - 2)/(x2 + 3x - 10) – x/(x + 5) = 4
Show how you get the answers {-3.8, 2}, yet only one of them is a true solution.

Answer 1

(x - 2)/(x^2 + 3x - 10) – x/(x + 5) = 4

(x-2)/[(x+5)(x-2)] - x/(x+5) = 4

1/(x+5) -x/(x+5) = 4

1-x = 4x+20

5 x = -19

x = 3.8

x = 2 does not satisfy the original equation and I do not know where you got it. If x = 2 then the denominator of the first term x^2+3x-10 = 0 so it is undefined.

Answer 2

Thanks a bunch. It makes sense. I was adding too many steps in and confusing myself.