• # question_answer What is the value of x in $1+{{\left\{ \frac{1}{1+\frac{1}{\left( 1+\frac{1}{x} \right)}} \right\}}^{=\,\frac{11}{7}?}}$ A)  1 B)  ½ C)  3 D)  7/11

Given that, $1+\frac{1}{\left\{ 1+\frac{1}{1+\frac{1}{x}} \right\}}=\frac{11}{7}$ $\Rightarrow$ $1+\frac{1}{\left( 1+\frac{x}{x+1} \right)}=\frac{11}{7}$ $\Rightarrow$ $1+\frac{1+x}{2x+1}=\frac{11}{7}$ $\Rightarrow$ $\frac{1+2x+1+x}{1+2x}=\frac{11}{7}$ $\Rightarrow$ $\frac{2+3x}{1+2x}=\frac{11}{7}$ $\Rightarrow$ $14+21x=11+22x$ $\therefore$ $x=14-11=3$