Question 196719
{{{((y^2 - y-2)/(y^2-6y-7))/((y^2+7y+12)/(y^2-4y-21))}}} Start with the given expression.



{{{((y^2-y-2)/(y^2-6y-7))((y^2-4y-21)/(y^2+7y+12))}}} Multiply the first fraction {{{(y^2-y-2)/(y^2-6y-7)}}} by the reciprocal of the second fraction {{{(y^2+7y+12)/(y^2-4y-21)}}}.



{{{(((y+1)(y-2))/(y^2-6y-7))((y^2-4y-21)/(y^2+7y+12))}}} Factor {{{y^2-y-2}}} to get {{{(y+1)(y-2)}}}.



{{{(((y+1)(y-2))/((y+1)(y-7)))((y^2-4y-21)/(y^2+7y+12))}}} Factor {{{y^2-6y-7}}} to get {{{(y+1)(y-7)}}}.



{{{(((y+1)(y-2))/((y+1)(y-7)))(((y+3)(y-7))/(y^2+7y+12))}}} Factor {{{y^2-4y-21}}} to get {{{(y+3)(y-7)}}}.



{{{(((y+1)(y-2))/((y+1)(y-7)))(((y+3)(y-7))/((y+4)(y+3)))}}} Factor {{{y^2+7y+12}}} to get {{{(y+4)(y+3)}}}.



{{{((y+1)(y-2)(y+3)(y-7))/((y+1)(y-7)(y+4)(y+3))}}} Combine the fractions. 



{{{(highlight((y+1))(y-2)highlight((y+3))highlight((y-7)))/(highlight((y+1))highlight((y-7))(y+4)highlight((y+3)))}}} Highlight the common terms. 



{{{(cross((y+1))(y-2)cross((y+3))cross((y-7)))/(cross((y+1))cross((y-7))(y+4)cross((y+3)))}}} Cancel out the common terms. 



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



So {{{((y^2 - y-2)/(y^2-6y-7))/((y^2+7y+12)/(y^2-4y-21))}}} simplifies to {{{(y-2)/(y+4)}}}.



In other words, {{{((y^2 - y-2)/(y^2-6y-7))/((y^2+7y+12)/(y^2-4y-21))=(y-2)/(y+4)}}} where {{{y<>-4}}}, {{{y<>-3}}}, {{{y<>-1}}}, or {{{y<>7}}}