Q 4. - Precalculus Enhanced with Graphing Utilities

Question

Simplify : $\frac{{\displaystyle \frac{1}{x}}+1}{{\displaystyle \frac{1}{x^2}}-1}$

Step-by-Step Solution

Answer

Simplified answer is $\frac{x}{1-x}$

Step 1. Given information

Given that $\frac{{\displaystyle \frac{1}{x}}+1}{{\displaystyle \frac{1}{x^2}}-1}$

Step 2. Simplification

$\Rightarrow \frac{{\displaystyle \frac{1}{x}}+1}{{\displaystyle \frac{1}{x^2}}-1}=\frac{x^2\left(1+x\right)}{x\left(1-x^2\right)}$

$\Rightarrow \frac{{\displaystyle \frac{1}{x}}+1}{{\displaystyle \frac{1}{x^2}}-1}=\frac{x\left(1+x\right)}{\left(1+x\right)\left(1-x\right)}$

$\Rightarrow \frac{{\displaystyle \frac{1}{x}}+1}{{\displaystyle \frac{1}{x^2}}-1}=\frac{x}{1-x}$