Q. 7.9 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1 . Given information

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

Step 2 . Simplify

$$\begin{gathered} \frac{5x}{x^2+5x+6}·\frac{x^2-4}{10x}=\frac{5x}{(x+3)(x+2)}·\frac{(x-2)(x+2)}{(5\times 2)x} \text{ Factorize numerator and denominator } \\ =\frac{5x(x-2)(x+2)}{\left(5\right)\left(2\right)x(x+3)(x+2)} \text{ Multiply numerator and denominator} \\ =\frac{(x-2)}{2(x+3)} \text{ Remove common factors of numerator and denominator} \end{gathered}$$

Hence, the given expression is simplified as $\frac{(x-2)}{2(x+3)}.$