Q 2. - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

Domain of the function should be $\frac{x-1}{x+4}>0$, therefore $(x-1)$ and $(x+4)$ must remain either positive or negative simultaneously.

For, $(x-1)>0$, the value of $x$ should be $(1,\infty )$ and $(x+4)>0$, the value of $x$ should be $(-4,\infty )$

Again, $(x-1)<0$, the value of $x$ should be $(-\infty ,1)$ and $(x+4)<0$, the value will be $(-\infty ,-4)$

Hence, the solution is $x\in (-\infty ,-4) \cup (-4,+\infty )$

Step 1. Given information

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

Step 2. Calculation

Solving the inequalities, the function consists all real number excepts $(-4)$, the domain will be $(-\infty ,-4) \cup (-4,+\infty )$.