If $$A = \frac{{x - 1}}{{x + 1}},$$   then the value of $$A - \frac{1}{A}$$  is:

A. $$\frac{{{x^2} - 1}}{{ - 4\left( {2x + 1} \right)}}$$

B. $$\frac{{ - 4x}}{{{x^2} - 1}}$$

C. $$\frac{{{x^2} - 1}}{{ - 4\left( {2x - 1} \right)}}$$

D. $$\frac{{ - 4\left( {2x - 1} \right)}}{{{x^2} - 1}}$$

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & A = \frac{{x - 1}}{{x + 1}} \cr & \frac{1}{A} = \frac{{x + 1}}{{x - 1}} \cr & A - \frac{1}{A} = \frac{{{{\left( {x - 1} \right)}^2} - {{\left( {x + 1} \right)}^2}}}{{{x^2} - 1}} \cr & A - \frac{1}{A} = \frac{{ - 4x}}{{{x^2} - 1}} \cr} $$