SOLUTION: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Rational Algebraic Exp

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Question 169906This question is from textbook Algebra and Trigonometry
: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Rational Algebraic Expression
Simplify
x^4-2x^2y^2+y^4 over x^4-x^3y-xy^3+y^4 This question is from textbook Algebra and Trigonometry

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E4-2x%5E2y%5E2%2By%5E4%29%2F%28x%5E4-x%5E3y-xy%5E3%2By%5E4%29
Group terms in the denominator:
%28x%5E4-2x%5E2y%5E2%2By%5E4%29%2F%28%28x%5E4-x%5E3y%29-%28xy%5E3-y%5E4%29%29
%28x%5E4-2x%5E2y%5E2%2By%5E4%29%2F%28x%5E3%28x-y%29-y%5E3%28x-y%29%29
%28x%5E4-2x%5E2y%5E2%2By%5E4%29%2F%28x-y%29%28x%5E3-y%5E3%29
Factoring the numerator:
%28x%5E2-y%5E2%29%28x%5E2-y%5E2%29%2F%28x-y%29%28x%5E3-y%5E3%29
%28x-y%29%28x%2By%29%28x%5E2-y%5E2%29%2F%28x-y%29%28x%5E3-y%5E3%29
%28x%2By%29%28x%5E2-y%5E2%29%2F%28x%5E3-y%5E3%29
Applying factor for "difference of cubes" in the denominator:
%28x%2By%29%28x%5E2-y%5E2%29%2F%28x-y%29%28x%5E2-xy%2By%5E2%29
%28x%2By%29%28x-y%29%28x%2By%29%2F%28x-y%29%28x%5E2-xy%2By%5E2%29
%28x%2By%29%28x%2By%29%2F%28x%5E2-xy%2By%5E2%29
%28x%2By%29%5E2%2F%28x%5E2-xy%2By%5E2%29