Perform the indicated operation and simplify?

Question

(4x)/(x-2)+(8)/(x+2)

Answer 1

Multiply the first fraction by the denominator of second and vie versa:
4x(x+2)/(x^2-4)+8(x-2)/(x^2-4)

=(4x^2+8x+8x+16)/(x^2-4)

You can do a little more from here, but this exerise does not yield a very pretty answer.

Remember that (a^2)-(b^2) = (a-b)(a+b)

Answer 2

Minor ammendment: I see how the first sentence can be misleading. You multiply both numerator and denominator, not just the numerator.