SOLUTION: please help me divide this rational expression x^2+6x+9/2x^2y-18y / 6xy+18y/3x^2y-27y

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Question 192413: please help me divide this rational expression
x^2+6x+9/2x^2y-18y / 6xy+18y/3x^2y-27y
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+6x+9/2x^2y-18y / 6xy+18y/3x^2y-27y
---
[(x+3)^2] / [2y(x-3)(x+3)] / [6y(x+3)] / 3y(x-3)(x+3)]
Do some canceling before inverting the denominator:
= [(x+3)/[2y(x-3)] / [2/(x-3)]
Invert the denominator and multiply
= [(x+3)/[2y(x-3)] * [(x-3)/2]
Cancel factors common to a numerator and a denominator:
= [(x+3)/[2(2y)]
= (x+3)/(4y)
=================
Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
divide this rational expression
%28x%5E2%2B6x%2B9%29%2F%282x%5E2y-18y%29
-----------
%286xy%2B18y%29%2F%283x%5E2y-27y%29
:
Factor
%28%28x%2B3%29%28x%2B3%29%29%2F%282y%28x%5E2-9%29%29
-----------
%286y%28x%2B3%29%29%2F%283y%28x%5E2-9%29%29
:
Cancel 3y into 6y, (the denominator fraction), factor (x^2-9)'s
%28%28x%2B3%29%28x%2B3%29%29%2F%282y%28x-3%29%28x%2B3%29%29
-----------
%282%28x%2B3%29%29%2F%28%28x%2B3%29%28x-3%29%29
:
Cancel the x+3's, (both fractions)
%28%28x%2B3%29%29%2F%282y%28x-3%29%29
-----------
2%2F%28%28x-3%29%29
:
Invert the dividing fraction and multiply, cancel (x-3)'s
%28%28x%2B3%29%29%2F%282y%28x-3%29%29 * %28x-3%29%2F2 = %28x%2B3%29%2F%284y%29 is the solution