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 $\frac{2}{3}$

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

Consider L.H.S

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

$\frac{1}{1/1-x}=1-x$

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

Equating with RHS

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

$2x=2-x$

$3x=2$

$x=\frac{2}{3}$