# Thread: Help with Rational Expression

1. ## Help with Rational Expression

Hello, everybody. I got the gist of rational expressions I think, at least on a basic level, but I'm having trouble with this particular one:

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

$\frac {-11x^2 + 10x - 16}{-x^3 + x^2 + 6x + 8}$

However, the actual solution is this, according to the solutions portion of the text I'm learning from:

$\frac {11x^2 - 18x + 8}{(2 + x)(2 - x)^2}$

I came up with my "solution" by finding the LCD by factoring every denominator of the three fractional operands and then multiplying them all by each other, then multiplying the numerators by those missing pieces of the factored denominators from the other operands. Then, I tried to simplify everything down, but I think I screwed up somewhere. I would greatly appreciate if someone could help me out by either giving me a set of instructions or showing the process of solving this problem step-by-step. :] Thanks a lot in advance.

Colton

2. Originally Posted by Noegddgeon
Hello, everybody. I got the gist of rational expressions I think, at least on a basic level, but I'm having trouble with this particular one:

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

$\frac {-11x^2 + 10x - 16}{-x^3 + x^2 + 6x + 8}$

However, the actual solution is this, according to the solutions portion of the text I'm learning from:

$\frac {11x^2 - 18x + 8}{(2 + x)(2 - x)^2}$

I came up with my "solution" by finding the LCD by factoring every denominator of the three fractional operands and then multiplying them all by each other, then multiplying the numerators by those missing pieces of the factored denominators from the other operands. Then, I tried to simplify everything down, but I think I screwed up somewhere. I would greatly appreciate if someone could help me out by either giving me a set of instructions or showing the process of solving this problem step-by-step. :] Thanks a lot in advance.

Colton
$\frac {7}{x+2} - \frac {x + 8}{4 - x^2} + \frac {3x - 2}{4 - 4x + x^2} = \frac {7}{x+2} + \frac {x + 8}{x^2-4} + \frac {3x - 2}{4 - 4x + x^2} =$ $~~\frac {7x^2-28x+28+x^2+8x-2x-16+3x^2+6x-2x-4}{(x+2)(x-2)^2}$