Question 147447
{{{(2x^2y-6xy^2+12xy)/(2xy)}}} Start with the given expression.



{{{(2x^2y)/(2xy)-(6xy^2)/(2xy)+(12xy)/(2xy)}}} Break up the fraction.



{{{(2x*x*y)/(2xy)-(6x*y*y)/(2xy)+(12xy)/(2xy)}}} Expand. Remember, {{{x^2=x*x}}} and {{{y^2=y*y}}}



{{{(2x*x*y)/(2xy)-(2*3*x*y*y)/(2xy)+(2*6*xy)/(2xy)}}} Factor 6 to get 2*3 and factor 12 to get 2*6. Notice how I'm factoring out 2's from each number.





{{{(highlight(2)highlight(x)*x*highlight(y))/(highlight(2)*highlight(x)highlight(y))-(highlight(2)*3*highlight(x)*highlight(y)*y)/(highlight(2)highlight(x)highlight(y))+(highlight(2)*6*highlight(xy))/(highlight(2)highlight(xy))}}} Highlight the common terms.




{{{(cross(2)cross(x)*x*cross(y))/(cross(2)*cross(x)cross(y))-(cross(2)*3*cross(x)*cross(y)*y)/(cross(2)cross(x)cross(y))+(cross(2)*6*cross(xy))/(cross(2)cross(xy))}}} Cancel out the common terms.



{{{x-3y+6}}} Simplify.



So {{{(2x^2y-6xy^2+12xy)/(2xy)}}} simplifies to {{{x-3y+6}}}



In other words, {{{(2x^2y-6xy^2+12xy)/(2xy)=x-3y+6}}} where {{{x<>0}}} or {{{y<>0}}}