Question 150628

{{{((z^2-64)/(z))/((z-8)/(z+5))}}} Start with the given expression.



{{{((z^2-64)/(z))((z+5)/(z-8))}}} Multiply the first fraction {{{(z^2-64)/(z)}}} by the reciprocal of the second fraction {{{(z-8)/(z+5)}}}.



{{{(((z-8)(z+8))/(z))((z+5)/(z-8))}}} Factor {{{z^2-64}}} to get {{{(z-8)*(z+8)}}}.



{{{((z-8)(z+8)(z+5))/(z(z-8))}}} Combine the fractions. 



{{{(highlight((z-8))(z+8)(z+5))/(z*highlight((z-8)))}}} Highlight the common terms. 



{{{(cross((z-8))(z+8)(z+5))/(z*cross((z-8)))}}} Cancel out the common terms. 



{{{((z+8)(z+5))/(z)}}} Simplify. 



So {{{((z^2-64)/(z))/((z-8)/(z+5))}}} simplifies to {{{((z+8)(z+5))/(z)}}}.



In other words, {{{((z^2-64)/(z))/((z-8)/(z+5))=((z+8)(z+5))/(z)}}} where {{{z<>0}}}, {{{z<>-5}}}, or {{{z<>8}}}