Question 151083
{{{((y^2)/(y-7))((y^2-5y-14)/(y^2+4y))}}} Start with the given expression.



{{{((y*y)/(y-7))((y^2-5y-14)/(y^2+4y))}}} Factor {{{y^2}}} to get {{{y*y}}}.



{{{((y*y)/(1(y-7)))(((y+2)*(y-7))/(y^2+4y))}}} Factor {{{y^2-5y-14}}} to get {{{(y+2)(y-7)}}}.



{{{((y*y)/(y-7))(((y+2)*(y-7))/(y*(y+4)))}}} Factor {{{y^2+4y}}} to get {{{y(y+4)}}}.



{{{(y*y(y+2)*(y-7))/(y(y-7)(y+4))}}} Combine the fractions. 



{{{(highlight(y)*y(y+2)highlight((y-7)))/(highlight(y)highlight((y-7))(y+4))}}} Highlight the common terms. 



{{{(cross(y)*y(y+2)cross((y-7)))/(cross(y)cross((y-7))(y+4))}}} Cancel out the common terms. 



{{{(y(y+2))/(y+4)}}} Simplify. 



{{{(y^2+2y)/(y+4)}}} Distribute



So {{{((y^2)/(y-7))((y^2-5y-14)/(y^2+4y))}}} simplifies to {{{(y^2+2y)/(y+4)}}}.



In other words, {{{((y^2)/(y-7))((y^2-5y-14)/(y^2+4y))=(y^2+2y)/(y+4)}}} where {{{y<>0}}}, {{{y<>-4}}}, or {{{y<>7}}}