Question

How do you solve `x/(x+2)-(x+2)/(x-2)=(x+3)/(x-2)`?

Answer 1

`x=-1` and `x=-10`

Explanation:

We have, at first, `(x)/(x+2) - (x+2)/(x-2) = (x+3)/(x-2)`.
We pass `-(x+2)/(x-2)` to the other side adding.
We now have`(x)/(x+2) = (x+3)/(x-2) + (x+2)/(x-2)`.
As the denominator is common on both fractions of the right side, we add them.
We get `(x)/(x+2) = (2x + 5)/(x-2)`.
We now cross multiply to get `x(x-2) = (x+2)(2x+5)`.
We multiply and get `x^2 - 2x = 2x^2 + 9x + 10`.
We pass the left hand side working to the right, getting `x^2 + 11x + 10 = 0` as an answer.
We factorise to get `(x+1)(x+10) = 0`.
Therefore, the answers are `x = -1` and `x = -10`.
Hope it helps :D .