If $A=\frac{1+2x}{1-2x}$ and $B =\frac{1-2x}{1+2x}$, then the value of $\frac{A+B}{A-B}$ is:

$x+\frac{1}{4x}$

If $A=\frac{1+2x}{1-2x}$ and $B =\frac{1-2x}{1+2x}$, then the value of $\frac{A+B}{A-B}$ is =

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

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

Put the value of x = 1 and satisfy from the equation,

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

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

Now, $\frac{A+B}{A-B}$  = $\frac{-3-\frac{1}{3}}{-3+\frac{1}{3}}$ = \(\frac{10}{8}\) = \(\frac{5}{4}\)

Checking the options,

$x+\frac{1}{4x}$ = $1+\frac{1}{4(1)}$ = \(\frac{5}{4}\) ( satisfied)

The value of $\frac{A+B}{A-B}$ is= $x+\frac{1}{4x}$