Question 151635
{{{(6x^2y^2 + 9xy^2) /(3xy)}}} Start with the given expression.



{{{(6x^2y^2) /(3xy) + (9xy^2) /(3xy)}}} Break up the fraction



{{{(2*3*x*x*y*y) /(3xy) + (3*3*x*y*y) /(3xy)}}} Expand. Remember, {{{6x^2y^2=2*3*x*x*y*y}}} and {{{9xy^2=3*3*x*y*y}}}



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



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



{{{2xy+3y}}} Simplify



So {{{(6x^2y^2 + 9xy^2) /(3xy)}}} simplifies to {{{2xy+3y}}}



In other words, {{{(6x^2y^2 + 9xy^2) /(3xy)=2xy+3y}}} where {{{x<>0}}} and {{{y<>0}}}