Chapter 5.2, Problem 4AYU

To determine

To find: The simplified form of the given equation.

Answer to Problem 4AYU

Thesimplified form is $\frac{x}{\left(1-x\right)}$ .

Explanation of Solution

Given:

The given equation is $\frac{\frac{1}{x}+1}{\frac{1}{x^2}-1}$ .

Calculation:

Consider the given equation is,

  $\frac{\frac{1}{x}+1}{\frac{1}{x^2}-1}$

Simplify the above equation as,

  $\begin{array}{c}\frac{\frac{1}{x}+1}{\frac{1}{x^2}-1}=\frac{\frac{1+x}{x}}{\frac{1-x^2}{x^2}}\\ =\frac{\left(1+x\right)x^2}{\left(1-x^2\right)x}\\ =\frac{\left(1+x\right)x}{\left(1+x\right)\left(1-x\right)}\\ =\frac{x}{\left(1-x\right)}\end{array}$