Question 715231
I am not sure if you meant {{{(x/y)(x^2) + (x/y) (y^2)}}} or {{{x/y (x^2) + x/y (y^2)}}} 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:
{{{(x/y)(x^2) + (x/y) (y^2)=(x/y)(x^2+y^2)}}} (taking out {{{(x/y)}}} as a common factor)
We can work from there to equivalent expressions that could also be the intended answer:
{{{(x/y)(x^2+y^2)=x(x^2+y^2)/y=(x^3+xy^2)/y=x^3/y+xy}}}
To me, all of those expressions seem simpler than the original one.
You could go directly to the last one
{{{(x/y)(x^2) + (x/y) (y^2)=x^3/y+xy^2/y=x^3/y+xy}}} by "performing indicated operations."
 
If the problem was not that, maybe this will help:
{{{x/y (x^2) + x/y (y^2)=(x/y)(1/x^2) + (x/y) (1/y^2)=(x/y)(1/x^2+1/y^2)}}} (taking out {{{(x/y)}}} as a common factor)
We can work from there to equivalent expressions that could also be the intended answer:
{{{(x/y)(1/x^2+1/y^2)=(x/y)((y^2+x^2)/x^2y^2)=x(x^2+y^2)/y/x^2y^2=(x^2+y^2)/xy^3=x/y^3+1/xy}}}
For this proble, you could go directly to the last expression by "performing indicated operations."