Question

Simplify the expression$\frac{5x^2+10x-75}{4x^2-24x-28}\cdot \frac{2x^2-10x-28}{x^2+7x+10}$

Short answer

The simplified value of expression is$\frac{5\left(x-3\right)}{2\left(x+1\right)}$

Step-by-step solution

Step 1. Write down the given expression.

The given expression is$\frac{5x^2+10x-75}{4x^2-24x-28}\cdot \frac{2x^2-10x-28}{x^2+7x+10}$

Step 2. Simplify the expression.

The given expression $\frac{5x^2+10x-75}{4x^2-24x-28}\cdot \frac{2x^2-10x-28}{x^2+7x+10}$is simplified as:

$\begin{array}{c}\frac{5x^2+10x-75}{4x^2-24x-28}\cdot \frac{2x^2-10x-28}{x^2+7x+10}=\frac{5\left(x^2+2x-15\right)}{4\left(x^2-6x-7\right)}\cdot \frac{2\left(x^2-5x-14\right)}{x^2+7x+10}\\ =\frac{5\left(x+5\right)\left(x-3\right)}{4\left(x-7\right)\left(x+1\right)}\cdot \frac{2\left(x-7\right)\left(x+2\right)}{\left(x+5\right)\left(x+2\right)}\\ =\frac{5}{2}\cdot \frac{\left(x-7\right)\left(x+2\right)\left(x+5\right)\left(x-3\right)}{\left(x+5\right)\left(x+2\right)\left(x-7\right)\left(x+1\right)}\\ =\frac{5\left(x-3\right)}{2\left(x+1\right)}\end{array}$

Step 3. Conclusion.

The simplified value of expression is$\frac{5\left(x-3\right)}{2\left(x+1\right)}$