Question

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

Short answer

Simplified answer is$\frac{x}{1-x}$

Step-by-step solution

Step 1. Given information

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

Step 2. Simplification

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

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

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