SOLUTION: Ahhhh, I am a pretty good math student and this question is probably not something I will see on my test but it's driving me nuts, please help... {{{((x-1)/(x^2-4))/(1+1/(x-2))}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Ahhhh, I am a pretty good math student and this question is probably not something I will see on my test but it's driving me nuts, please help... {{{((x-1)/(x^2-4))/(1+1/(x-2))}      Log On


   

Question 722693: Ahhhh, I am a pretty good math student and this question is probably not something I will see on my test but it's driving me nuts, please help...
%28%28x-1%29%2F%28x%5E2-4%29%29%2F%281%2B1%2F%28x-2%29%29%22%22-%22%221%2F%28x-2%29
The book says the answer is 4/(x+2)(x-2) but I keep getting -3/(x+2)(x-2).
I am obviously handling the second term incorrectly but if some one could show me the work I know I'll get it.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x-1%29%2F%28x%5E2-4%29%29%2F%281%2B1%2F%28x-2%29%29%22%22-%22%221%2F%28x-2%29

Do the left numerator by factoring the denominator:

               %28x-1%29%2F%28x%5E2-4%29 = %28x-1%29%2F%28%28x-2%29%28x%2B2%29%29

Do the left denominator by getting an LCD of (x-2):

               1%2B1%2F%28x-2%29 = %28x-2%29%2F%28x-2%29%22%22%2B%22%221%2F%28x-2%29 = %28x-2%2B1%29%2F%28x-2%29 = %28x-1%29%2F%28x-2%29

So we have

%28%28x-1%29%2F%28%28x-2%29%28x%2B2%29%29%29%2F%28%28x-1%29%2F%28x-2%29%29%22%22-%22%221%2F%28x-2%29

The first term is a fraction divided by a fraction, so

%28x-1%29%2F%28%28x-2%29%28x%2B2%29%29%22%F7%22%28x-1%29%2F%28x-2%29%22%22-%22%221%2F%28x-2%29

So we invert the second fraction and change the division to 
multiplication.

%28x-1%29%2F%28%28x-2%29%28x%2B2%29%29%22%2A%22%28x-2%29%2F%28x-1%29%22%22-%22%221%2F%28x-2%29

We cancel the (x-2)'s

%28x-1%29%2F%28%28cross%28x-2%29%29%28x%2B2%29%29%22%2A%22%28cross%28x-2%29%29%2F%28x-1%29%22%22-%22%221%2F%28x-2%29

We cancel the (x-1)'s

%28%22%22%5E1cross%28x-1%29%29%2F%28%28cross%28x-2%29%29%28x%2B2%29%29%22%2A%22%28cross%28x-2%29%29%2F%28cross%28x-1%29%29%22%22-%22%221%2F%28x-2%29


1%2F%28x%2B2%29%22%22-%22%221%2F%28x-2%29

Get an LCD of (x+2)(x-2)

%281%2Ared%28%28x-2%29%29%29%2F%28%28x%2B2%29%2Ared%28%28x-2%29%29%29%22%22-%22%22%281%2Ared%28%28x%2B2%29%29%29%2F%28%28x-2%29%2Ared%28%28x%2B2%29%29%29


%28%28x-2%29-%28x%2B2%29%29%2F%28%28x%2B2%29%2A%28x-2%29%29

%28x-2-x-2%29%2F%28%28x%2B2%29%2A%28x-2%29%29

%28cross%28x%29-2-cross%28x%29-2%29%2F%28%28x%2B2%29%2A%28x-2%29%29

%28-2-2%29%2F%28%28x%2B2%29%2A%28x-2%29%29

%28-4%29%2F%28%28x%2B2%29%2A%28x-2%29%29

So the answer has -4 in the numerator, not +4.

Edwin