Chapter 4.6, Problem 15AYU

In Problems 15-18, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 7-10 of Section 4.5.]

Solve $R\left(x\right)>0$, where $R\left(x\right)=\frac{x+1}{x\left(x+4\right)}$.

To determine

To find: The inequality by using the graph of the function $R\left(x\right)>0$.

Answer to Problem 15AYU

$\left\{x|-4<x<-1\text{ or }x>0\right\}$

Explanation of Solution

Given:

$R\left(x\right)=\frac{x+1}{x\left(x+4\right)}$

From the graph, we can see that $R\left(x\right)>0$ for $-4<x<-1$ or $x>0$. The solution set is $\left\{x|-4<x<-1\text{ or }x>0\right\}$ or, using interval notation, $\left(-4,-1\right)\cup \left(0,\infty \right)$.