Question

Simplify $\frac{9x^2}{x^2+11x+30}·\frac{x^2-36}{3x^2}$.

Short answer

The simplest form of the given expression is$\frac{3(x-6)}{(x+5)}.$

Step-by-step solution

Step 1. Given information

The given expression is$\frac{9x^2}{x^2+11x+30}·\frac{x^2-36}{3x^2}.$

Step 2. Simplify

$$\begin{gathered} \frac{9x^2}{x^2+11x+30}·\frac{x^2-36}{3x^2}=\frac{3·3·x·x}{(x+5)(x+6)}·\frac{(x-6)(x+6)}{3·x·x}\text{Factorizenumeratoranddenominator} \\ =\frac{3·3·x·x(x-6)(x+6)}{3·x·x(x+5)(x+6)}\text{Multiply}\mathrm{numerator}\mathrm{and}\mathrm{denominator} \\ =\frac{3(x-6)}{(x+5)}\text{Removethecommonfactorsofnumeratoranddenominator} \end{gathered}$$

Hence, the given expression is simplified as$\frac{3(x-6)}{(x+5)}.$