Question 162413
I'll do the first one to get you started


{{{(yx^2)/(x-y)+(xy^3)/(xy-x^2) }}} Start with the given expression



{{{(yx^2)/(x-y)+(xy^3)/(-x(x-y)) }}} Factor the second denominator



{{{(yx^2)/(x-y)-(xy^3)/(x(x-y)) }}} Simplify



So we can see that the LCD is {{{x(x-y)}}}. So we need to multiply the first fraction by {{{x/x}}} to get the denominator to the LCD



{{{(x/x)((yx^2)/(x-y))-(xy^3)/(x(x-y)) }}} Multiply the first fraction by {{{x/x}}}



{{{(x(yx^2))/(x(x-y))-(xy^3)/(x(x-y)) }}} Combine the fractions



{{{(x^3y)/(x(x-y))-(xy^3)/(x(x-y)) }}} Multiply



{{{(x^3y-xy^3)/(x(x-y))}}} Combine the fractions



So {{{(yx^2)/(x-y)+(xy^3)/(xy-x^2) }}} simplifies to {{{(x^3y-xy^3)/(x(x-y))}}}