Expert: Richard J. Raridon - 6/2/2008

Question
i have a question... how do i simplify this?
1/x+y - 1/x-y + 2x/x^2-y^2

how do i add/subtract these?

also...
How do i state these restrictions?
x + x/x-2 = 2/x-2

x/x-3 - 7/x+5 = 24/x^2+2x-15

Answer
1. For clarity you should write it 1/(x+y) -1/(x-y) +2x(x^2-y^2).
Multiply each term by (x^2-y^2) to get 1(x-y) -1(x+y) +2x =2x-2y
2. x +x/(x-2) = 2/(x-2)
Multiply each term by (x-2) to get x(x-2)+x = 2  or x^2-x-2=0 or
(x-2)(x+1)= 0 and x = 2,-1
3. Multiply each term by x^2+2x-15 to get
x(x+5) -7(x-3) = 24 or x^2-2x-3=0 = (x-3)(x+1) so x = 3,-1