How to add/subtract this rational expression and to find its excluded values?

Question

(x-2)/(x+2) + 1/(x²-4) - (x+2)/(2-x)

I got stuck while simplifying the third term..

Answer 1

Factors the denominator:

(x-2)/(x+2) + 1/(x+2)(x-2) - (x+2)/(2-x)

Changes the sign in the last fraction:

(x-2)/(x+2) + 1/(x+2)(x-2) + (x+2)/(x-2)

LCD is (x+2)(x-2):

(x-2)(x-2) + 1 + (x+2)(x+2) over (x+2)(x-2)

x^2-4 + 1 + x^2 +4 over x^2-4

2x^2+1 over x^2-4