Question

What is the value of $x$ in $1+\frac{1}{1+\left\{\frac{1}{1+\frac{1}{x}}\right\}}=\frac{11}{7}$?

• A. $1$
• B. $3$
• C. $\frac{1}{2}$
• D. $\frac{7}{11}$

Answer 1

The correct option is B $3$

$1+\frac{1}{1+\left[\frac{1}{(1+\frac{1}{x})}\right]}=\frac{11}{7}\Rightarrow 1+\frac{1}{1+\frac{x}{1+x}}=\frac{11}{7}$

$\Rightarrow 1+\frac{1+x}{1+x+x}=\frac{11}{7}\Rightarrow \frac{(1+2x)+(1+x)}{(1+2x)}=\frac{11}{7}$

$\Rightarrow 7(2+3x)=11(1+2x)\Rightarrow 14+21x=11+22x$

$\Rightarrow x=3$