Q.2 - Precalculus Enhanced with Graphing Utilities

Question

Solve the inequality $\frac{x-1}{x+4}>0$.

Step-by-Step Solution

Answer

The solution is $\left(-\infty ,-4\right)\cup \left(1,\infty \right)$.

Step 1. Given information.

Consider the given information,

$\frac{x-1}{x+4}>0$

Step 2. Solve the inequality.

First, put the denominator equal to zero.

$\begin{array}{rcl}x+4& =& 0\\ x& =& -4\end{array}$

Now, put the denominator equal to zero.

$\begin{array}{rcl}x-1& =& 0\\ x& =& 1\end{array}$

Write the intervals, $\left(-\infty ,-4\right)\cup \left(1,\infty \right)$