The value of frac{1}{2+frac{1}{2+frac{1}{2-fr | vedclass

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(D) To solve the expression $\frac{1}{2+\frac{1}{2+\frac{1}{2-\frac{1}{2}}}}$,we simplify from the bottom up.First,simplify the innermost fraction: $2

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$\frac{8}{19}$

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(D) To solve the expression $\frac{1}{2+\frac{1}{2+\frac{1}{2-\frac{1}{2}}}}$,we simplify from the bottom up.First,simplify the innermost fraction: $2 - \frac{1}{2} = \frac{4-1}{2} = \frac{3}{2}$.Now,substitute this back into the expression: $\frac{1}{2+\frac{1}{2+\frac{1}{3/2}}} = \frac{1}{2+\frac{1}{2+\frac{2}{3}}}$.Next,simplify the denominator $2 + \frac{2}{3} = \frac{6+2}{3} = \frac{8}{3}$.Substitute this back: $\frac{1}{2+\frac{1}{8/3}} = \frac{1}{2+\frac{3}{8}}$.Finally,simplify the denominator $2 + \frac{3}{8} = \frac{16+3}{8} = \frac{19}{8}$.Thus,the expression becomes $\frac{1}{19/8} = \frac{8}{19}$.

The value of $\frac{1}{2+\frac{1}{2+\frac{1}{2-\frac{1}{2}}}}$ is

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