SOLUTION: Hi, I've been having trouble with this problem for days. Perform the indicated operations and express the answer in simplest form: n/n-2 + n+3/n+7 + 15n+69/n^2+5n-14 I got

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Question 856935: Hi, I've been having trouble with this problem for days.
Perform the indicated operations and express the answer in simplest form:
n/n-2 + n+3/n+7 + 15n+69/n^2+5n-14
I got the factors as (n+7)(n-2) and then multiplied each so that the denominators would be the same. I then got: (n)(n+7)+(n+3)(n-2)+15n+69.
=n^2+7n+n^2-2n+3n-6+15n+69
=2n^2+23n+63/(n+7)(n+2)
Thank you for your help!!

Found 3 solutions by stanbon, Fombitz, richwmiller:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
n/n-2 + n+3/n+7 + 15n+69/n^2+5n-14
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I got the factors as (n+7)(n-2) and then multiplied each so that the denominators would be the same. I then got: (n)(n+7)+(n+3)(n-2)+15n+69.
=n^2+7n+n^2-2n+3n-6+15n+69
= [2n^2+23n+63]/(n+7)(n+2)
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That is correct.
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Cheers,
Stan H.
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Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website!

<--- This matches your answer but you can factor this.

Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website!

Since (n^2+5n-14)=(n+7)(n-2)
But you changed the sign 2n^2+23n+63/(n+7)(n+2)
It should be (n-2) not (n+2)
2n^2+23n+63/(n+7)(n-2)
2n^2+23n+63=(2n+9) (n+7)
(n-2) /(n-2) cancels out and we have
It all reduces to
(2n+9)/(n-2) when n is not -7