## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

The simplified form of the rational expression $\frac{5}{x+7}\cdot \frac{x+7}{10}$ is $\frac{1}{2}$.
Consider the provided rational expression, $\frac{5}{x+7}\cdot \frac{x+7}{10}$ The quotient rule for two rational expressions is, $\frac{A}{B}\div \frac{C}{D}=\frac{A}{B}\cdot \frac{D}{C}$ So, multiply the divisor, $\frac{5}{x+7}\cdot \frac{x+7}{10}=\frac{5\left( x+7 \right)}{\left( x+7 \right)10}$ Regroup and remove the factor equal to 1, \begin{align} & \frac{5}{x+7}\cdot \frac{x+7}{10}=\frac{\left( 5 \right)\left( x+7 \right)}{\left( x+7 \right)\left( 10 \right)} \\ & =\frac{\left( x+7 \right)\left( 5 \right)}{\left( x+7 \right)\left( 10 \right)} \\ & =1\cdot \frac{\left( 1 \right)}{\left( 2 \right)} \\ & =\frac{1}{2} \end{align}