If x=12, then find the value of x+11+11+1x

x+11+11+1x=12+11+11+2=12+11+13=12+143=12+34=54

If x=12, then find the value of x+11+11+1x

x+11+11+1x=12+11+11+2=12+11+13=12+143=12+34=54

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

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$\frac{5}{2}$

$\frac{3}{4}$

$\frac{5}{4}$

$\frac{3}{2}$

answer is A.

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Detailed Solution

$x + \frac{1}{1 + \frac{1}{1 + \frac{1}{x}}} = \frac{1}{2} + \frac{1}{1 + \frac{1}{1 + 2}} = \frac{1}{2} + \frac{1}{1 + \frac{1}{3}}$
$\begin{array}{l} = \frac{1}{2} + \frac{1}{\frac{4}{3}} \\ = \frac{1}{2} + \frac{3}{4} = \frac{5}{4} \end{array}$

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