okay so I'm trying to answer this question for precal but its telling me I'm wrong so maybe someone else can understand it

problem: x/x-2 + 12/x+2 =8/x^2-4
and I got it down to x+16/x+2 by factoring but now what

the first thing you do is find a common denominator on the left side, wich is (x+2)(x-2)
then you need to add everything up and you should get x^2+2x+12x-24 all divided by (x+2)(x-2) which should simplify to 12x

do the same thing on the right hand side of the equation... find a common denominator which is x^2.

then you should simplify that and you should get 12x=(8-4x^2)/x^2

cross multiply and solve. I got it down to 12x^3 +4x^2-8=0

if you have a graphing calculator try and solve it, I'm too lazy right now, but you reminded me to go study calculus.

Multiply through by the LCD, which is (x+2)(x-2)

(x+2)(x-2)\cdot\frac{x}{x-2}+(x+2)(x-2)\cdot\frac{12}{x+2}=(x+2)(x-2)\cdot\frac{8}{(x+2)(x-2)}

As you can see, we have lots of cancellations and we get rid of the fractions.

x^{2}+14x-32=0

Solve the quadratic. You will get two solutions. Only one may be good. Check.

That that sounds better that my post from earlier. Oh a great website is calc101.com for factoring and stuff like that