Math Help - Help with adding and subtracting rational expressions

1. Help with adding and subtracting rational expressions

I've been having trouble with this equation for a little while. I cannot get the answer that's in the answer key and have no idea where I'm going wrong. If someone could please show their calculations I'd really appreciate it.

$\frac{7}{x+2}-\frac{x+8}{4-x^2}+\frac{3x-2}{4-4x+x^2}$

2. Re: Help with adding and subtracting rational expressions

$\frac{7}{x+2}-\frac{x+8}{4-x^2}+\frac{3x-2}{4-4x+x^2}$

$\frac{7}{x+2}-\frac{x+8}{(2-x)(2+x)}+\frac{3x-2}{(x-2)^2}$

$\frac{7}{x+2}+\frac{x+8}{(x-2)(x+2)}+\frac{3x-2}{(x-2)^2}$

$\frac{7(x-2)^2}{(x-2)^2(x+2)}+\frac{(x+8)(x-2)}{(x-2)^2(x+2)}+\frac{(3x-2)(x+2)}{(x-2)^2(x+2)}$

$\frac{7(x-2)^2 + (x+8)(x-2) + (3x-2)(x+2)}{(x-2)^2(x+2)}$

can you finish from here?

3. Re: Help with adding and subtracting rational expressions

Thanks so much! When I multiplied the second term by -1/1 to change (2-x)(2+x) to (x-2)(x+2) I was changing the numerator from -x+8 to x-8. That problem was really getting to me. Thanks again!