<PRE><B>Question 279539</B>
the question is find the reciprocals of three consecutive even integers
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1st even: 2x-2
2nd even: 2x
3rd even: 2x+2
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Reciprocals:
1st: 1/(2x-2)
2nd: 1/2x
3rd: 1/(2x+2)
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Add them.
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1/(2(x-1)) + 1/2x + 1/2(x+1)
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lcd = 2x(x^2-1)
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Rewrite each fraction with the lcd as its denominator:
(x+1)/lcd + (x^2-1)/lcd + (x-1)/lcd
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Combine the numerators over the lcd:
[x + 1 + x^2-1 + x-1]/lcd
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Simplify the numerator:
[x^2 +2x -1]/[x^2-1]
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Cheers,
Stan H.
</PRE>