Question

If $\frac{2x}{1+\frac{1}{1+\frac{x}{1-x}}}=1$ then find the value of $\frac{x+1}{4x-2}$

• A. $\frac{1}{2}$
• B. $\frac{5}{2}$
• C. $\frac{7}{2}$
• D. None of these

Answer 1

Answer: (B)

$\frac{5}{2}$

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

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

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

$2x=2-x$

$3x=2$

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

Then $\frac{x+1}{4x-2}=\frac{\frac{2}{3}+1}{\frac{8}{3}-2}=\frac{5}{2}$