Question

Simplify$\frac{5x}{x^2+5x+6}·\frac{x^2-4}{10x}$.

Short answer

The simplest form of the given expression is$\frac{(x-2)}{2(x+3)}.$

Step-by-step solution

Step 1. Given information

The given expression is$\frac{5x}{x^2+5x+6}·\frac{x^2-4}{10x}$

Step 2. Simplify

$$\begin{gathered} \frac{5x}{x^2+5x+6}·\frac{x^2-4}{10x}=\frac{5x}{(x+3)(x+2)}·\frac{(x-2)(x+2)}{(5\times 2)x}\text{Factorizenumeratoranddenominator} \\ =\frac{5x(x-2)(x+2)}{\left(5\right)\left(2\right)x(x+3)(x+2)}\text{Multiplynumeratoranddenominator} \\ =\frac{(x-2)}{2(x+3)}\text{Removecommonfactorsofnumeratoranddenominator} \end{gathered}$$

Hence, the given expression is simplified asrole="math" localid="1644999982152" $\frac{(x-2)}{2(x+3)}.$