Question 216450
Please help me solve this problem:
<pre><font size = 4 color = "indigo"><b>
{{{(3x^4+3x^(-3)y+18x^(-2)y^2)/(12xy^3+3y^4)}}}

Factor out the GCF which in the numerator includes
3 and the smallest power term of x, which is {{{x^(-3)}}}.

{{{(3x^(-3)(x^7+y+6xy^2))/(3y^3(4x+y))}}}

{{{(cross(3)x^(-3)(x^7+y+6xy^2))/(cross(3)y^3(4x+y))}}}

{{{(x^(-3)(x^7+y+6xy^2))/(y^3(4x+y))}}}

The reason I got the {{{x^7}}} was because I subtracted the
exponent I was taking OUT from the exponent I was taking
it OUT OF, i.e., {{{4-(-3)=4+3=7}}}. For a similar reason, I got
{{{x^1}}} in the term {{{6xy^2}}} from {{{-2-(-3)=-2+3=1}}}.   

Then we bring the {{{x^(-3)}}} to the bottom as {{{x^3}}}

{{{(x^7+y+6xy^2)/(x^3y^3(4x+y))}}}

Edwin</pre></font></b>