SOLUTION: 1+ 2/x+ 4/x2+ 8/x3 ___________ ______ 1- 16/x4

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Question 103185: 1+ 2/x+ 4/x2+ 8/x3
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1- 16/x4
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.%281%2B+2%2Fx%2B+4%2Fx2%2B+8%2Fx3%29%2F%281-+16%2Fx4%29
Multiply top and bottom by x%5E4
%28x%5E4%2B+2x%5E3%2B+4x%5E2%2B+8x%29%2F%28x%5E4-16%29
x%28x%5E3%2B+2x%5E2%2B+4x%2B+8%29%2F%28x%5E4-16%29
Let's look at the denominator first.
%28x%5E4-16%29=%28x%5E2%2B4%29%28x%5E2-4%29
%28x%5E4-16%29=%28x%5E2%2B4%29%28x%2B2%29%28x-2%29
Now the numerator
x%28x%5E3%2B2x%5E2%2B4x%2B8%29%29=x%28x%5E2%2B4%29%28x%2B2%29
Let's substitute
x%28x%5E3%2B+2x%5E2%2B+4x%2B+8%29%2F%28x%5E4-16%29

x%2F%28x-2%29
Good idea to check the answer
Let's try x=3
Equation 1 gives an answer
1.Numerator=%281%2B+2%2F3%2B+4%2F9%2B+8%2F27%29
1.Denominator=%281-+16%2F81%29
Numerator = 2.470407
Denominator = 0.802469
Numerator/Denominator = 3
x%2F%28x-2%29=3%2F%283-2%29
x%2F%28x-2%29=3
3=3
Good answer.
%281%2B+2%2Fx%2B+4%2Fx2%2B+8%2Fx3%29%2F%281-+16%2Fx4%29=x%2F%28x-2%29