Answer
$\dfrac{2cy}{b}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the complex fraction, $
\dfrac{\dfrac{45xyz}{24ab}}{\dfrac{30xz}{32ac}}
,$ multiply the numerator by the reciprocal of the denominator. Then cancel any common factors between the numerator and the denominator.
$\bf{\text{Solution Details:}}$
Using $\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\div\dfrac{c}{d},$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{45xyz}{24ab}\div\dfrac{30xz}{32ac}
.\end{array}
To divide the fractions above, get the reciprocal of the divisor and change the operator to multiplication. Hence, the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{45xyz}{24ab}\cdot\dfrac{32ac}{30xz}
\\\\=
\dfrac{45\cancel{x}y\cancel{z}}{24\cancel{a}b}\cdot\dfrac{32\cancel{a}c}{30\cancel{x}\cancel{z}}
\\\\=
\dfrac{45y}{24b}\cdot\dfrac{32c}{30}
\\\\=
\dfrac{\cancel{15}(3)y}{24b}\cdot\dfrac{32c}{\cancel{15}(2)}
\\\\=
\dfrac{3y}{24b}\cdot\dfrac{32c}{2}
\\\\=
\dfrac{3y}{\cancel{8}(3)b}\cdot\dfrac{\cancel{8}(4)c}{2}
\\\\=
\dfrac{3y}{3b}\cdot\dfrac{4c}{2}
\\\\=
\dfrac{\cancel{3}y}{\cancel{3}b}\cdot\dfrac{\cancel{2}(2)c}{\cancel{2}}
\\\\=
\dfrac{2cy}{b}
.\end{array}
