I need to solve the following equation for the variable x.
4/x-2+1/x+2=7x/x^2-4
I have a feeling you meant to type
4/(x-2) + 1/(x+2) = 7x/(x^2-4)
in that case, multiply each term by x^2-4 to get
4(x+2) + (x-2) = 7x
4x + 8 + x - 2 = 7x
-2x = -6
x = 3