SOLUTION: Please help me simplify this complex rational expression: 6/x^2-4 - 5/x+2 ___________ _____ 7/x^2-4 - 4/x-2

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Question 107649This question is from textbook Intermediate Algebra
: Please help me simplify this complex rational expression:
6/x^2-4 - 5/x+2
_________________
7/x^2-4 - 4/x-2 This question is from textbook Intermediate Algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume you mean:
6%2F%28%28x%5E2-4%29%29 - 5%2F%28%28x%2B2%29%29
-------------------
7%2F%28%28x%5E2-4%29%29 - 4%2F%28%28x-2%29%29
:
Note that (x^2 - 4) can be factored to (x+2)(x-2)
That will the common denominator for both the numerator & denominator fractions.
:
%286+-+5%28x-2%29%29%2F%28%28x-2%29%28x%2B2%29%29
------------- =
%287+-+4%28x%2B2%29%29%2F%28%28x%2B2%29%28x-2%29%29
:
:
Multiply what's inside the brackets
%286+-+5x+%2B+10%29%2F%28%28x-2%29%28x%2B2%29%29
----------------- =
%287+-+4x+-+8%29%2F%28%28x%2B2%29%28x-2%29%29
:
:
%2816+-+5x%29%2F%28%28x-2%29%28x%2B2%29%29
----------------- =
%28-1+-+4x%29%2F%28%28x%2B2%29%28x-2%29%29
:
:
Invert the dividing fraction and multiply:
%2816+-+5x%29%2F%28%28x-2%29%28x%2B2%29%29 * %28%28x%2B2%29%28x-2%29%29%2F%28-1+-+4x%29
:
Cancel (x+2)(x-2) and you have:
%2816-5x%29%2F%28-1+-+4x%29
:
Did this help you? Any questions?