SOLUTION: Please please help. I have asked this question three times cansomeone help me.\ Write a rational expression, in its simpliest form, that represents the sum of the reciprocals of t

Algebra ->  Rational-functions -> SOLUTION: Please please help. I have asked this question three times cansomeone help me.\ Write a rational expression, in its simpliest form, that represents the sum of the reciprocals of t      Log On


   

Question 87738: Please please help. I have asked this question three times cansomeone help me.\
Write a rational expression, in its simpliest form, that represents the sum of the reciprocals of the squares of the consecutive even intergers n-2, n, and n+2. That is the expression should be in terms of the interger variable n.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write a rational expression, in its simplest form, that represents the sum of the reciprocals of the squares of the consecutive even integers n-2, n, and n+2. That is the expression should be in terms of the integer variable n.
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Assume this problem means:
1%2F%28%28n-2%29%5E2%29 + 1%2Fn%5E2 + 1%2F%28%28n%2B2%29%5E2%29
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Place the expression over a single denominator:

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FOIL all those squares:

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Multiply (n^2-4n+4)(n^2+4n+4) the vertical way, you should get:
n%5E4+-+8n%5E2+%2B+16+; then we have:

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Group like terms in the numerator and mult in the denominator:
=
:
%283n%5E4%2B16%29%2F%28n%5E6-8n%5E4%2B16n%5E2%29 is what I get here, hope this helps you.