Question 146498

{{{(z^2-7z+10)/(z^2+4z-45)}}} Start with the given expression.



{{{((z-2)*(z-5))/(z^2+4z-45)}}} Factor {{{z^2-7z+10}}} to get {{{(z-2)*(z-5)}}}.



{{{((z-2)*(z-5))/((z+9)*(z-5))}}} Factor {{{z^2+4z-45}}} to get {{{(z+9)*(z-5)}}}.



{{{((z-2)highlight(z-5))/((z+9)highlight(z-5))}}} Highlight the common terms. 



{{{((z-2)cross(z-5))/((z+9)cross(z-5))}}} Cancel out the common terms. 



{{{((z-2))/((z+9))}}} Simplify. 



So {{{(z^2-7z+10)/(z^2+4z-45)}}} simplifies to {{{(z-2)/(z+9)}}}.



In other words, {{{(z^2-7z+10)/(z^2+4z-45)=(z-2)/(z+9)}}} where {{{z<>-9}}} or {{{z<>5}}}