A. \(\frac{3}{7}\) B. \(\frac{7}{3}\) C. \(\frac{3}{7}\) D. \(\frac{7}{3}\)
Correct Answer: C
Explanation
\( \frac{1}{1+\frac{1}{x}}=\frac{1}{\left(\frac{x+1}{x}\right)}=\frac{x}{x+1}\)dding I to this result. we have \(1+\frac{x}{x+1}=\frac{2 x+1}{x+1}\) So that. \(\frac{1}{1+\frac{1}{1+\frac{1}{x}}}=\frac{x+1}{2 x+1}\)inally adding 1 to this. we have \begin{aligned} 1+\frac{x+1}{2 x+1} &=\frac{2 x+1+x+1}{2 x+1} \\ &=\frac{3 x+2}{2 x+1} \end{aligned} we then equate this to 5 i.e \begin{aligned} \Rightarrow \frac{3 x+2}{2 x+1} &=5 \\ 3 x+2 &=10 x+5 \\ -7 x &=3 \\ x &=-\frac{7}{3} \end{aligned}