Question

Simplify the expression$\frac{\frac{5x^2-5x-30}{45-15x}}{\frac{6+x-x^2}{4x-12}}$

Short answer

The simplified value of expression is $\frac{4}{3}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is$\frac{\frac{5x^2-5x-30}{45-15x}}{\frac{6+x-x^2}{4x-12}}$

Step 2. Simplify the expression.

The given expression $\frac{\frac{5x^2-5x-30}{45-15x}}{\frac{6+x-x^2}{4x-12}}$is simplified as:

$\begin{array}{c}\frac{\frac{5x^2-5x-30}{45-15x}}{\frac{6+x-x^2}{4x-12}}=\frac{5x^2-5x-30}{45-15x}\times \frac{4x-12}{6+x-x^2}\\ =\frac{5\left(x^2-x-6\right)}{15\left(3-x\right)}\times \frac{4\left(3-x\right)}{\left(x^2-x-6\right)}\\ =\frac{4}{3}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{4}{3}$.