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 ->  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

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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(12704) 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.
:
Assume this problem means:
1%2F%28%28n-2%29%5E2%29 + 1%2Fn%5E2 + 1%2F%28%28n%2B2%29%5E2%29
:
Place the expression over a single denominator:
%28%28n%5E2%28n%2B2%29%5E2%29+%2B+%28%28n-2%29%5E2%2A%28n%2B2%29%5E2%29+%2B+%28n%5E2%28n-2%29%5E2%29%29%2Fn%5E2%28n-2%29%5E2%28n%2B2%29%5E2%29
:
FOIL all those squares:
%28n%5E2%28n%5E2%2B4n%2B4%29+%2B+%28n%5E2-4n%2B4%29%28n%5E2%2B4n%2B4%29+%2B+n%5E2%28n%5E2-4n%2B4%29%29%2F%28n%5E2%28n%5E2-4n%2B4%29%28n%5E2%2B4n%2B4%29%29
:
Multiply (n^2-4n+4)(n^2+4n+4) the vertical way, you should get:
n%5E4+-+8n%5E2+%2B+16+; then we have:
%28%28n%5E4%2B4n%5E3%2B4n%5E2%29+%2B+%28n%5E4-8n%5E2%2B16%29+%2B+%28n%5E4-4n%5E3%2B4n%5E2%29%29%2F%28n%5E2%28n%5E4-8n%5E2%2B16%29%29
:
Group like terms in the numerator and mult in the denominator:
%28n%5E4%2Bn%5E4%2Bn%5E4%2B4n%5E3-4n%5E3%2B4n%5E2-8n%5E2%2B4n%5E2%2B16%29%2F%28n%5E6-8n%5E4%2B16n%5E2%29 =
:
%283n%5E4%2B16%29%2F%28n%5E6-8n%5E4%2B16n%5E2%29 is what I get here, hope this helps you.