Question 150627

{{{((z^2-49)/(z))/((z+7)/(z+9))}}} Start with the given expression.



{{{((z^2-49)/(z))((z+9)/(z+7))}}} Multiply the first fraction {{{(z^2-49)/(z)}}} by the reciprocal of the second fraction {{{(z+7)/(z+9)}}}.



{{{(((z-7)(z+7))/(z))((z+9)/(z+7))}}} Factor {{{z^2-49}}} to get {{{(z-7)(z+7)}}}.



{{{((z-7)(z+7)(z+9))/(z(z+7))}}} Combine the fractions. 



{{{((z-7)highlight((z+7))(z+9))/(z*highlight((z+7)))}}} Highlight the common terms. 



{{{((z-7)cross((z+7))(z+9))/(z*cross((z+7)))}}} Cancel out the common terms. 



{{{((z-7)(z+9))/(z)}}} Simplify. 



So {{{((z^2-49)/(z))/((z+7)/(z+9))}}} simplifies to {{{((z-7)(z+9))/(z)}}}.



In other words, {{{((z^2-49)/(z))/((z+7)/(z+9))=((z-7)(z+9))/(z)}}} where {{{z<>0}}}, {{{z<>-7}}}, or {{{z<>-9}}}