SOLUTION: In class we are adding and subtracting rational expressions with unlike denominators. It is a pun puzzle worksheet. I get the idea and can do most of the problems, but there are so

Question 415512: In class we are adding and subtracting rational expressions with unlike denominators. It is a pun puzzle worksheet. I get the idea and can do most of the problems, but there are some like the one I am going to ask about that are stumping me.
So the expression is:
u 2u
----- + -------------
u + 5 u^2 + 8u + 15
So, the first step is to find the LCM by factoring the denominators.
u + 5 = (u + 5)
u^2 + 8u + 15 = (u + 5)(u + 3)
LCM: (u + 5)(u + 3)
So now I have gotten the LCM, I must make the denominators like, like so:
u (u + 3) 2u u^2 + 3u 2u
----- x ---------- + -------------- = -------------- + --------------
u + 5 (u + 3) (u + 5)(u + 3) (u + 5)(u + 3) (u + 5)(u + 3)
Now, I combine my like terms which gives me:
u^2 + 5u
--------------
(u + 5)(u + 3)
However, on the worksheet, there are other possible answers listed along with the correct answer to each question to solve the puzzle. The problem is that my answer does not appear in the answer box. The answer that does appear is:
u^2 - 7
--------------
(u + 3)(u + 5)
The only reason I think that that is the answer you are supposed to get is because it is the only answer listed with a matching denominator. My question is, how can you get a negative ( - 7 ) in an answer from an expression that is entirely positive?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
denominators. It is a pun puzzle worksheet. I get the idea and can do most of the problems, but there are some like the one I am going to ask about that are stumping me.
So the expression is:
u 2u
----- + -------------
u + 5 u^2 + 8u + 15
So, the first step is to find the LCM by factoring the denominators.
u + 5 = (u + 5)
u^2 + 8u + 15 = (u + 5)(u + 3)
LCM: (u + 5)(u + 3)
So now I have gotten the LCM, I must make the denominators like, like so:
u (u + 3) 2u u^2 + 3u 2u
----- x ---------- + -------------- = -------------- + --------------
u + 5 (u + 3) (u + 5)(u + 3) (u + 5)(u + 3) (u + 5)(u + 3)
Now, I combine my like terms which gives me:
u^2 + 5u
--------------
(u + 5)(u + 3)

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