Question

if $\frac{2x}{1+\frac{1}{1+\frac{x}{1-x}}}$ = 1, then find the value of x.

• A. $1$
• B. $\frac{4}{3}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is D $\frac{2}{3}$

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

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

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

$\Rightarrow$ $\frac{2x}{2-x}=1$

$\Rightarrow$ $2x=2-x$

$\Rightarrow$ $3x=2$

$\Rightarrow$ $\frac{3}{2}$