SOLUTION: Please help me solve this problem: 3x^4+3x^-3y+18x^-2y^2 ______________________ 12xy^3+3y^4

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Question 216450: Please help me solve this problem:
3x^4+3x^-3y+18x^-2y^2
______________________
12xy^3+3y^4

Answer by Edwin McCravy(6936) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this problem:

%283x%5E4%2B3x%5E%28-3%29y%2B18x%5E%28-2%29y%5E2%29%2F%2812xy%5E3%2B3y%5E4%29

Factor out the GCF which in the numerator includes
3 and the smallest power term of x, which is x%5E%28-3%29.

%283x%5E%28-3%29%28x%5E7%2By%2B6xy%5E2%29%29%2F%283y%5E3%284x%2By%29%29

%28cross%283%29x%5E%28-3%29%28x%5E7%2By%2B6xy%5E2%29%29%2F%28cross%283%29y%5E3%284x%2By%29%29

%28x%5E%28-3%29%28x%5E7%2By%2B6xy%5E2%29%29%2F%28y%5E3%284x%2By%29%29

The reason I got the x%5E7 was because I subtracted the
exponent I was taking OUT from the exponent I was taking
it OUT OF, i.e., 4-%28-3%29=4%2B3=7. For a similar reason, I got
x%5E1 in the term 6xy%5E2 from -2-%28-3%29=-2%2B3=1.   

Then we bring the x%5E%28-3%29 to the bottom as x%5E3

%28x%5E7%2By%2B6xy%5E2%29%2F%28x%5E3y%5E3%284x%2By%29%29

Edwin