Question

In the following exercises, divide the rational expressions.

$\frac{x^2+3x-10}{4x}÷\left(2x^2+20x+50\right)$

Short answer

The simplified rational expression is$\frac{\left(x-2\right)}{8x\left(x+5\right)}.$

Step-by-step solution

Step 1. Given Information

$\frac{x^2+3x-10}{4x}÷\left(2x^2+20x+50\right)$

$=\frac{x^2+3x-10}{4x}\times \frac{1}{2x^2+20x+50}$

Step 2. Factors the numerator and denominator 

$$\begin{gathered} =\frac{\left(x+5\right)\left(x-2\right)}{4x}\times \frac{1}{2\left(x+5\right)\left(x+5\right)} \\ =\frac{\left(x+5\right)\left(x-2\right)}{2\times 4x\left(x+5\right)\left(x+5\right)} \end{gathered}$$

Step 3. Remove the common factors 

$=\frac{\left(x-2\right)}{8x\left(x+5\right)}$