SOLUTION: Can you simplify x/y (x^2) + x/y (y^2)

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Question 715231: Can you simplify x/y (x^2) + x/y (y^2)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I am not sure if you meant %28x%2Fy%29%28x%5E2%29+%2B+%28x%2Fy%29+%28y%5E2%29 or x%2Fy+%28x%5E2%29+%2B+x%2Fy+%28y%5E2%29 so I will work on both of them.
I am also not sure what your book (or teacher) means by "simplify" so I will work toward expressions that seem simpler to me, and may or may not be more useful, depending on circumstances.

I suspect the problem and the expected answer is this:
%28x%2Fy%29%28x%5E2%29+%2B+%28x%2Fy%29+%28y%5E2%29=%28x%2Fy%29%28x%5E2%2By%5E2%29 (taking out %28x%2Fy%29 as a common factor)
We can work from there to equivalent expressions that could also be the intended answer:

To me, all of those expressions seem simpler than the original one.
You could go directly to the last one
%28x%2Fy%29%28x%5E2%29+%2B+%28x%2Fy%29+%28y%5E2%29=x%5E3%2Fy%2Bxy%5E2%2Fy=x%5E3%2Fy%2Bxy by "performing indicated operations."

If the problem was not that, maybe this will help:
(taking out %28x%2Fy%29 as a common factor)
We can work from there to equivalent expressions that could also be the intended answer:

For this proble, you could go directly to the last expression by "performing indicated operations."