If A = x - 1x + 1, then the value of A - 1/A is:

Answer: Option B

$$\begin{array}{rl}& A=\frac{x-1}{x+1}\\ & \frac{1}{A}=\frac{x+1}{x-1}\\ & A-\frac{1}{A}=\frac{{\left(x-1\right)}^2-{\left(x+1\right)}^2}{x^2-1}\\ & A-\frac{1}{A}=\frac{-4x}{x^2-1}\end{array}$$