Question 166665

# 1




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



{{{(4z)/(4(2z-3))}}} Factor the GCF {{{4}}} from {{{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}}}



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# 2




{{{(y^5-3y^3+8y^2)/(5y)}}} Start with the given expression.



{{{(y^2(y^3-3y+8))/(5y)}}} Factor the GCF {{{y^2}}} from {{{y^5-3y^3+8y^2}}} to get {{{y^2*(y^3-3*y+8)}}}.



{{{(y*y(y^3-3y+8))/(5y)}}} Factor {{{y^2}}} to get {{{y*y}}}



{{{(y*highlight(y)(y^3-3y+8))/(5*highlight(y))}}} Highlight the common terms. 



{{{(y*cross(y)(y^3-3y+8))/(5*cross(y))}}} Cancel out the common terms. 



{{{(y(y^3-3y+8))/(5)}}} Simplify



{{{(y^4-3y^2+8y)/(5)}}} Distribute



So {{{(y^5-3y^3+8y^2)/(5y)}}} simplifies to {{{(y^4-3y^2+8y)/(5)}}}.



In other words, {{{(y^5-3y^3+8y^2)/(5y)=(y^4-3y^2+8y)/(5)}}} where {{{y<>0}}}




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# 3


Are you sure that the numerator is not {{{z^3-4z^2}}} ???



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



{{{(z^2*(z-4))/(z^2-8z+16)}}} Factor the GCF {{{z^2}}} from {{{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)^2}}}.



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



{{{(z^2*cross(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}}}