Chapter 8, Problem 15SGR

To determine

To simplify: the expression

Answer to Problem 15SGR

The value of the expression is $\frac{\left(x-3\right)}{\left(x+1\right)}$

Explanation of Solution

Given information: The expression is $\frac{\frac{x^2+3x-18}{x+4}}{\frac{x^2+7x+6}{x+4}}$

Calculation:

  $\begin{array}{l}\frac{\frac{x^2+3x-18}{x+4}}{\frac{x^2+7x+6}{x+4}}\\ \Rightarrow \frac{x^2+3x-18}{x+4}·\frac{x+4}{x^2+7x+6}\\ \Rightarrow \frac{x^2+3x-18}{x^2+7x+6}\\ \Rightarrow \frac{\left(x+6\right)\left(x-3\right)}{\left(x+1\right)\left(x+6\right)}\\ \Rightarrow \frac{\left(x-3\right)}{\left(x+1\right)}\end{array}$