SOLUTION: Subtract and simplify completely: 4y^2-x^2 over x-y subtract -3y^2 over y-x

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Question 133506: Subtract and simplify completely:
4y^2-x^2 over x-y subtract -3y^2 over y-x
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%28%284y%5E2-x%5E2%29%2F%28x-y%29%29-%28%28-3y%5E2%29%2F%28y-x%29%29


The trick on this one is to note that x-y=-1%28y-x%29, so you can write:

%28%284y%5E2-x%5E2%29%2F%28x-y%29%29-%28%283y%5E2%29%2F%28x-y%29%29

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

%28%284y%5E2-x%5E2%29-%283y%5E2%29%29%2F%28x-y%29


Now combine like terms:
%28y%5E2-x%5E2%29%2F%28x-y%29


Now you have the difference of two squares in your numerator, so factor it:
%28%28y-x%29%28y%2Bx%29%29%2F%28x-y%29

Again note that x-y=-1%28y-x%29, so %28y-x%29%2F%28x-y%29=-1, and now you can write:

%28%28y-x%29%28y%2Bx%29%29%2F%28x-y%29=-%28y%2Bx%29 or -y-x if you prefer.