SOLUTION: What is z-1/z-8 - z+1/z+8 + z-120/z^2-64 ?

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Question 347966: What is z-1/z-8 - z+1/z+8 + z-120/z^2-64 ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28z-1%29%2F%28z-8%29+-+%28z%2B1%29%2F%28z%2B8%29+%2B+%28z-120%29%2F%28z%5E2-64%29 Start with the given expression.


Factor the last denominator.


Multiply the first fraction by %28z%2B8%29%2F%28z%2B8%29


Multiply the second fraction by %28z-8%29%2F%28z-8%29


FOIL


%28z%5E2%2B7z-8-+%28z%5E2-7z-8%29%2Bz-120%29%2F%28z%5E2-64%29 Combine the fractions.


%28z%5E2%2B7z-8-+z%5E2%2B7z%2B8%2Bz-120%29%2F%28z%5E2-64%29 Distribute.


%2815z-120%29%2F%28z%5E2-64%29 Combine like terms.


%2815%28z-8%29%29%2F%28z%5E2-64%29 Factor the numerator.


%2815%28z-8%29%29%2F%28%28z-8%29%28z%2B8%29%29 Factor the numerator.


%2815%2Across%28%28z-8%29%29%29%2F%28cross%28%28z-8%29%29%28z%2B8%29%29 Cancel out the common terms.


15%2F%28z%2B8%29 Simplify.


So


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Jim