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

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

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

then the value of $A-\frac{1}{A}$ = ?

Put the value of x = 2

$A = \frac{2-1}{2+1}$ = \(\frac{1}{3}\)

Now put the value of A into the required equation,

$A-\frac{1}{A}$ = $\frac{1}{3}-\frac{3}{1}$ = $\frac{-8}{3}$

Now check from the options which option is satisfying the value by putting x = 2

If we choose,

$\frac{-4x}{x^2-1}$ = $\frac{-4×2}{2^2-1}$ = $\frac{-8}{3}$ (Satisfied)

So the value of $A-\frac{1}{A}$ = $\frac{-4x}{x^2-1}$