Question

In the following exercises, Divide the rational expression

$\frac{2y^2-10yz-48z^2}{2y-1}÷\left(4y^2-32yz\right)$

Short answer

The simplified expression is$\frac{2\left(y+3z\right)}{2y\left(2y-1\right)}$

Step-by-step solution

Step 1. Given Information

$$\begin{gathered} \frac{2y^2-10yz-48z^2}{2y-1}÷\left(4y^2-32yz\right) \\ =\frac{2y^2-10yz-48z^2}{2y-1}\times \frac{1}{\left(4y^2-32yz\right)} \end{gathered}$$

Step 2. Factor the numerator and denominators

$$\begin{gathered} =\frac{2\left(y+3z\right)\left(y-8z\right)}{2y-1}\times \frac{1}{4y\left(y-8z\right)} \\ =\frac{2\left(y+3z\right)\left(y-8z\right)}{4y\left(2y-1\right)\left(y-8z\right)} \end{gathered}$$

Step 3. Remove the common factors

$=\frac{2\left(y+3z\right)}{2y\left(2y-1\right)}$