4/(x-2) + 6/(x+2) = "-6x/(x" squared - 4)

Answer 1

Let me rewrite this to what I think the equation is:

4/(x-2) + 6/(x+2) = -6x/(x²-4)

The first step is here is recognize that (x²-4) can be factored into (x+2)(x-2). So we should multiply both sides of this equation with (x+2)(x-2) to get rid of the variables in the denominators. That would leave us with:

4(x+2) + 6(x-2) = -6x

Now we just need to simplify this equation:

4x + 8 + 6x - 12 = -6x

16x = 4

x = 1/4