SOLUTION: Perform the indicated operations and simplify. x-4/x-8 - x+1/x+8 + x-72/x^2 -64 These should look like 3 fractions.

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: Perform the indicated operations and simplify. x-4/x-8 - x+1/x+8 + x-72/x^2 -64 These should look like 3 fractions.      Log On

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Question 133103: Perform the indicated operations and simplify.
x-4/x-8 - x+1/x+8 + x-72/x^2 -64
These should look like 3 fractions.
Answer by vleith(2825) About Me  (Show Source):
You can put this solution on YOUR website!
Given: %28x-4%29%2F%28x-8%29+-+%28x%2B1%29%2F%28x%2B8%29+%2B+%28x-72%29%2F%28x%5E2+-64%29+
Simply:
In order to combine the three terms, you need to have a common denominator. In this case, the least common denominator is %28x%5E2+-64%29
So multiply the first term by %28x%2B8%29%2F%28x%2B8%29 and the second term by %28x-8%29%2F%28x-8%29+ (note both values are equal to 1.
This yields:

Now multiply out (expand) the numeratiors to get:
%28%28x%5E2+%2B+4x+-32%29+-+%28x%5E2+-7x+-8%29+%2B%28x-72%29%29%2F%28%28x-8%29%28x%2B8%29%29
Collect terms in the numerator to get:
%2812x+-96%29%2F%28%28x-8%29%28x%2B8%29%29
%2812%28x+-8%29%29%2F%28%28x-8%29%28x%2B8%29%29
%2812%29%2F%28%28x%2B8%29%29