Question 154268
# 1


{{{(4z)/(8z-12)}}} Start with the given expression.



{{{(4z)/(4(2z-3))}}} Factor {{{8z-12}}} to get {{{4(2z-3)}}}.



{{{(highlight(4)z)/(highlight(4)(2z-3))}}} Highlight the common terms. 



{{{(cross(4)z)/(cross(4)(2z-3))}}} Cancel out the common terms. 



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



So {{{(4z)/(8z-12)}}} simplifies to {{{(z)/(2z-3)}}}.



In other words, {{{(4z)/(8z-12)=(z)/(2z-3)}}} where {{{z<>3/2}}}



<hr>


# 2




{{{(z^3+4z^2)/(z^2+8z+16)}}} Start with the given expression.



{{{(z^2*(z+4))/(z^2+8z+16)}}} Factor {{{z^3+4z^2}}} to get {{{z^2*(z+4)}}}.



{{{(z^2*(z+4))/((z+4)(z+4))}}} Factor {{{z^2+8z+16}}} to get {{{(z+4)(z+4)}}}.



{{{(z^2highlight((z+4)))/(highlight((z+4))(z+4))}}} Highlight the common terms. 



{{{(z^2cross((z+4)))/(cross((z+4))(z+4))}}} Cancel out the common terms. 



{{{(z^2)/(z+4)}}} Simplify. 



So {{{(z^3+4z^2)/(z^2+8z+16)}}} simplifies to {{{(z^2)/(z+4)}}}.



In other words, {{{(z^3+4z^2)/(z^2+8z+16)=(z^2)/(z+4)}}} where {{{z<>-4}}}