Question 70035
{{{(7*x^5*y^5 - 21*x^4*y^4 + 14*x^3*y^3)/(7*x^3*y^3)}}}
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Notice that 7 can be factored from each of the terms in the numerator so that the problem
becomes:
.
{{{7*(x^5*y^5 -3*x^4*y^4 + 2*x^3*y^3)/(7*x^3*y^3)}}}
.
In this form it is easier to recognize that the multiplier 7 in the numerator cancels 
with the multiplier 7 in the denominator to reduce the problem to:
.
{{{(x^5*y^5 -3*x^4*y^4 + 2*x^3*y^3)/(x^3*y^3)}}}
.
Similarly, you can next factor an {{{x^3}}} from every term in the numerator to get:
.
{{{x^3*(x^2*y^5 -3*x*y^4 + 2*y^3)/(x^3*y^3)}}}
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Then notice that this {{{x^3}}} multiplier in the numerator cancels with the {{{x^3}}}
multiplier in the denominator.  This reduces the problem to:
.
{{{(x^2*y^5 -3*x*y^4 + 2*y^3)/(y^3)}}}
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Finally, you can factor a {{{y^3}}} from every term in the numerator to get:
.
{{{y^3*(x^2*y^2 -3*x*y + 2)/(y^3)}}}
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And recognize that the {{{y^3}}} multiplier of the numerator cancels with the {{{y^3}}} 
in the denominator to leave you with just:
.
{{{(x^2*y^2 -3*x*y + 2))}}}
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This might be the answer you were looking for, but notice also that this can be factored
into:
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{{{(xy - 2)*(xy - 1)}}}
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and maybe this is the answer form you were looking for.

Hope this helps you to see a form for dividing polynomials that might be useful.