Question 133506
{{{((4y^2-x^2)/(x-y))-((-3y^2)/(y-x))}}}



The trick on this one is to note that {{{x-y=-1(y-x)}}}, so you can write:


{{{((4y^2-x^2)/(x-y))-((3y^2)/(x-y))}}}


Now that you have the same denominator in both fractions, you can simply add the numerators:


{{{((4y^2-x^2)-(3y^2))/(x-y)}}}



Now combine like terms:
{{{(y^2-x^2)/(x-y)}}}



Now you have the difference of two squares in your numerator, so factor it:

{{{((y-x)(y+x))/(x-y)}}}


Again note that {{{x-y=-1(y-x)}}}, so {{{(y-x)/(x-y)=-1}}}, and now you can write:


{{{((y-x)(y+x))/(x-y)=-(y+x)}}} or {{{-y-x}}} if you prefer.