Question

Divide Rational Expressions:$\frac{24z^2}{2z\hspace{0.17em}-\hspace{0.17em}8}÷\frac{4z-28}{z^2-11z+28}$

Short answer

The required answer is$3z^2$.

Step-by-step solution

Step 1. Given information.

The given expression is$\frac{24z^2}{2z\hspace{0.17em}-\hspace{0.17em}8}÷\frac{4z-28}{z^2-11z+28}$.

Step 2.  Simplify the expression. 

$$\begin{gathered} \frac{24z^2}{2z\hspace{0.17em}-\hspace{0.17em}8}÷\frac{4z-28}{z^2-11z+28} \\ \frac{\frac{24z^2}{2z-8}}{\frac{4z-28}{z^2-11z+28}} \end{gathered}$$

Apply the fraction rule.

localid="1647859771425" $$\begin{gathered} =\frac{24z^2\left(z^2-11z+28\right)}{\left(2z-8\right)\left(4z-28\right)} \\ =\frac{2·\hspace{0.17em}12z^2\left(z^2-11z+28\right)}{2\left(z-4\right)\left(4z-28\right)} \\ =\frac{12z^2\left(z-4\right)\left(z-7\right)}{\left(z-4\right)\left(4z-28\right)} \\ =\frac{12z^2\left(z-7\right)}{4z-28} \\ =\frac{12z^2\left(z-7\right)}{4\left(z-7\right)} \\ =\frac{12z^2}{4} \\ =3z^2 \end{gathered}$$