SOLUTION: Can you help me solve this equation? I have tried to solve it for two days now and still can't get it right. {{{((x^-8)+(x^-16))/(1-x^-16)}}}

Algebra ->  Algebra  -> Exponents-negative-and-fractional -> SOLUTION: Can you help me solve this equation? I have tried to solve it for two days now and still can't get it right. {{{((x^-8)+(x^-16))/(1-x^-16)}}}      Log On

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Question 212536: Can you help me solve this equation? I have tried to solve it for two days now and still can't get it right.
%28%28x%5E-8%29%2B%28x%5E-16%29%29%2F%281-x%5E-16%29
Found 3 solutions by Alan3354, nerdybill, Theo:
Answer by Alan3354(21612) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%5E-8%29%2B%28x%5E-16%29%29%2F%281-x%5E-16%29
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It's not an equation, there's no equal sign, so there's nothing to solve for.
It can be simplified.
%28%28x%5E-8%29%2B%28x%5E-16%29%29%2F%281-x%5E-16%29
Multiply NUM and DEN by x^16
= %28x%5E8+%2B+1%29%2F%28x%5E16+-+1%29
= %28x%5E8+%2B+1%29%2F%28%28x%5E8+%2B+1%29%2A%28x%5E8+-+1%29%29
= 1%2F%28x%5E8+-+1%29

Answer by nerdybill(5413) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with:
.
%28%28x%5E-8%29%2B%28x%5E-16%29%29%2F%281-x%5E-16%29
.
.
Multiply by %28x%5E-16%29%2F%28x%5E-16%29:
.
%28%28x%5E-8%29%2B%28x%5E-16%29%29%2F%281-x%5E-16%29 * %28x%5E16%29%2F%28x%5E16%29
.
.
Doing so yields:
%28x%5E8%2B1%29%2F%28x%5E16-1%29
.
.
Now, factoring the denominator:
%28x%5E8%2B1%29%2F%28%28x%5E8-1%29%28x%5E8%2B1%29%29
.
Canceling like-terms we end up with:
1%2F%28x%5E8-1%29



Answer by Theo(2978) About Me  (Show Source):
You can put this solution on YOUR website!
as best I can determine, your answer would be:
1%2F%28x%5E8-1%29
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here's how:
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your equation is:
%28%28x%5E-8%29%2B%28x%5E-16%29%29%2F%281-x%5E-16%29
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since x%5E%28-a%29+=+1%2Fx%5Ea your equation becomes:
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your equation becomes:
%281%2Fx%5E8+%2B+1%2Fx%5E16%29%2F%281-1%2Fx%5E16%29
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multiply numerator and denominator by x%5E16 to get:
%28x%5E8%2B1%29%2F%28x%5E16-1%29
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factor denominator to get:
%28x%5E8%2B1%29%2F%28%28x%5E8%2B1%29%2A%28x%5E8-1%29%29
-----
equation becomes:
1%2F%28x%5E8-1%29