SOLUTION: z^2-64/z / z-8/z+5

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Question 150628: z^2-64/z / z-8/z+5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28z%5E2-64%29%2F%28z%29%29%2F%28%28z-8%29%2F%28z%2B5%29%29 Start with the given expression.


%28%28z%5E2-64%29%2F%28z%29%29%28%28z%2B5%29%2F%28z-8%29%29 Multiply the first fraction %28z%5E2-64%29%2F%28z%29 by the reciprocal of the second fraction %28z-8%29%2F%28z%2B5%29.


%28%28%28z-8%29%28z%2B8%29%29%2F%28z%29%29%28%28z%2B5%29%2F%28z-8%29%29 Factor z%5E2-64 to get %28z-8%29%2A%28z%2B8%29.


%28%28z-8%29%28z%2B8%29%28z%2B5%29%29%2F%28z%28z-8%29%29 Combine the fractions.


%28highlight%28%28z-8%29%29%28z%2B8%29%28z%2B5%29%29%2F%28z%2Ahighlight%28%28z-8%29%29%29 Highlight the common terms.


%28cross%28%28z-8%29%29%28z%2B8%29%28z%2B5%29%29%2F%28z%2Across%28%28z-8%29%29%29 Cancel out the common terms.


%28%28z%2B8%29%28z%2B5%29%29%2F%28z%29 Simplify.


So %28%28z%5E2-64%29%2F%28z%29%29%2F%28%28z-8%29%2F%28z%2B5%29%29 simplifies to %28%28z%2B8%29%28z%2B5%29%29%2F%28z%29.


In other words, where z%3C%3E0, z%3C%3E-5, or z%3C%3E8