Question 150626


{{{(z^2-8z+15)/(z^2+2z-35)}}} Start with the given expression.



{{{((z-3)*(z-5))/(z^2+2z-35)}}} Factor {{{z^2-8z+15}}} to get {{{(z-3)*(z-5)}}}.



{{{((z-3)*(z-5))/((z+7)*(z-5))}}} Factor {{{z^2+2z-35}}} to get {{{(z+7)*(z-5)}}}.



{{{((z-3)highlight(z-5))/((z+7)highlight(z-5))}}} Highlight the common terms. 



{{{((z-3)cross(z-5))/((z+7)cross(z-5))}}} Cancel out the common terms. 



{{{(z-3)/(z+7)}}} Simplify. 



So {{{(z^2-8z+15)/(z^2+2z-35)}}} simplifies to {{{(z-3)/(z+7)}}}.



In other words, {{{(z^2-8z+15)/(z^2+2z-35)=(z-3)/(z+7)}}} where {{{z<>-7}}} or {{{z<>5}}}