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)
$$\eqalign{ & A = \frac{{x - 1}}{{x + 1}} \cr & \frac{1}{A} = \frac{{x + 1}}{{x - 1}} \cr & A - \frac{1}{A} = \frac{{{{\left( {x - 1} \right)}^2} - {{\left( {x + 1} \right)}^2}}}{{{x^2} - 1}} \cr & A - \frac{1}{A} = \frac{{ - 4x}}{{{x^2} - 1}} \cr} $$This Question Belongs to Arithmetic Ability >> Algebra
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