Question 202585
{{{((4uz)/(3z))/((8u)/(9z))}}} Start with the given expression.



{{{((4uz)/(3z))*((9z)/(8u))}}} Multiply the first fraction by the reciprocal of the second fraction.



{{{((4uz)/(3z))*((3*3z)/(8u))}}} Factor the second numerator



{{{((4uz)/(3z))*((3*3z)/(2*4u))}}} Factor the second denominator
 


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



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



{{{z*(3/2)}}} Simplify



{{{(3z)/2}}} Rearrange the terms.



So {{{((4uz)/(3z))/((8u)/(9z))=(3z)/2}}}