SOLUTION: I do not know where to begin: 1/3-5/3x+2/x^2 divided by 1/3 - 3/x^2

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Question 134730: I do not know where to begin:
1/3-5/3x+2/x^2
divided by
1/3 - 3/x^2
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I assume this is the problem:
1%2F3-5%2F%283x%29%2B2%2Fx%5E2
---------------
1%2F3+-+3%2Fx%5E2
We want to get fractions over a common denominator; it will be 3x^2 on both:
%28%28x%5E2+%2B+5x+%2B+3%282%29%29%29%2F%283x%5E2%29
-------------
%28%28x%5E2+-+3%283%29%29%29%2F%283x%5E2%29
which is
%28%28x%5E2+%2B+5x+%2B+6%29%29%2F%283x%5E2%29
-------------
%28%28x%5E2+-+9%29%29%2F%283x%5E2%29
:
Invert the dividing fraction and multiply:
%28%28x%5E2+%2B+5x+%2B+6%29%29%2F%283x%5E2%29 * %283x%5E2%29%2F%28%28x%5E2+-+9%29%29
:
You can see the 3x^2's will cancel leaving us with:
%28%28x%5E2+%2B+5x+%2B+6%29%29%2F%28%28x%5E2+-+9%29%29
:
Both denominator and numerator will factor:
%28%28x%2B2%29%28x%2B3%29%29%2F%28%28x-3%29%28x%2B3%29%29%29
:
Cancel out (x+3) and you have:
%28%28x%2B2%29%29%2F%28%28x-3%29%29
:
How about this? Did it make sense to you?