SOLUTION: k + 4 + k^2 -5k + 8 ------- ------ ----------- --- = k + 1 1

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Question 636615: k + 4 + k^2 -5k + 8
------- ------ --------------- =
k + 1 1 - k k^2 -1
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
k 4 k^2 -5k + 8
------- + ------ + ------------
k + 1 1 - k k^2 -1

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Rewrite:
k 4 k^2 -5k + 8
------- - ------ + ------------
k + 1 k - 1 k^2 -1
lcm = (k^2-1)
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Rewrite each fraction with the lcm as its denominator:
------
[k(k-1) -4(k+1) +k^2-5k+8]/[k^2-1]
------
[k^2-k-4k-4+k^2-5k+8]/[k^2-1]
------
[2k^2-10k+8]/[k^2-1]
----
= [2(k^2-5k+4)]/[k^2-1]
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= [2(k-4)(k-1)]/[(k+1)(k-1)]
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= [2(k-4)]/[k+1]
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Cheers,
Stan H.
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SOLUTION: k + 4 + k^2 -5k + 8 ------- ------ ----------- --- = k + 1 1 - k k^2 -1