Question

Find the value of x.
$\frac{1}{1+\frac{1}{1-x}}=2$

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Answer 1

The correct option is C

3

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