SOLUTION: simplify (4x^4-9y^4)/(4x^4+12x^2y^2+9y^4)

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Question 443201: simplify (4x^4-9y^4)/(4x^4+12x^2y^2+9y^4)
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Notice that 4x^4 and 9y^4 are perfect squares.
(2x^2)^2 = 4x^4
(3y^2)^2 = 9y^4
We have the difference of squares:
Then, %284x%5E4+-+9y%5E4%29+=+%282x%5E2+%2B+3y%5E2%29%282x%5E2-3y%5E2%29
Noticing the same fact that 4x^4 and 9y^4 are perfect squares, and that (2*3)*2 = 12, we can say that %284x%5E4+%2B+12x%5E2y%5E2+%2B9y%5E4%29+=+%282x%5E2%2B3y%5E2%29%5E2
So we have %28%282x%5E2+%2B+3y%5E2%29%282x%5E2-3y%5E2%29%29%2F%282x%5E2%2B3y%5E2%29%5E2

%282x%5E2-3y%5E2%29%2F%282x%5E2%2B3y%5E2%29