Question 62

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

Solution

Given, $$A=\frac{x-1}{x+1}$$

$$A-\frac{1}{A}$$ = $$\frac{x-1}{x+1}-\frac{x+1}{x-1}$$

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

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

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

$$=\frac{-4x}{x^2-1}$$

Hence, the correct answer is Option D

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