Question 174198
{{{((9-n^2)/(n^2-5n+6))((n^2+2n-15)/(n^2+8n+15))}}} Start with the given expression.



{{{((-(n-3)*(n+3))/(n^2-5n+6))((n^2+2n-15)/(n^2+8n+15))}}} Factor {{{9-n^2}}} to get {{{-(n-3)*(n+3)}}}.



{{{((-(n-3)*(n+3))/((n-2)*(n-3)))((n^2+2n-15)/(n^2+8n+15))}}} Factor {{{n^2-5n+6}}} to get {{{(n-2)*(n-3)}}}.



{{{((-(n-3)*(n+3))/((n-2)*(n-3)))(((n+5)*(n-3))/(n^2+8n+15))}}} Factor {{{n^2+2n-15}}} to get {{{(n+5)*(n-3)}}}.



{{{((-(n-3)*(n+3))/((n-2)*(n-3)))(((n+5)*(n-3))/((n+5)*(n+3)))}}} Factor {{{n^2+8n+15}}} to get {{{(n+5)*(n+3)}}}.



{{{(-(n-3)*(n+3)(n+5)*(n-3))/((n-2)*(n-3)(n+5)*(n+3))}}} Combine the fractions. 



{{{-(highlight((n-3))highlight((n+3))highlight((n+5))(n-3))/((n-2)highlight((n-3))highlight((n+5))highlight((n+3)))}}} Highlight the common terms. 



{{{-(cross((n-3))cross((n+3))cross((n+5))(n-3))/((n-2)cross((n-3))cross((n+5))cross((n+3)))}}} Cancel out the common terms. 



{{{-(n-3)/(n-2)}}} Simplify. 



So {{{((9-n^2)/(n^2-5n+6))((n^2+2n-15)/(n^2+8n+15))}}} simplifies to {{{-(n-3)/(n-2)}}}.