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Addition of Fractions

Question

Simplify:
$1 + \frac{1}{1 + \frac{1}{1 + \frac{7}{5}}}$

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Solution

Verified by Toppr

$\begin{matrix} W e h a v e 1 + \frac{1}{1 + \frac{1}{1 + \frac{7}{5}}} = 1 + \frac{1}{1 + \frac{1}{\frac{5 + 7}{5}}} = 1 + \frac{1}{1 + \frac{5}{12}} = 1 + \frac{1}{\frac{12 + 5}{12}} = 1 + \frac{12}{17} = \frac{17 + 12}{17} = \frac{29}{17} \end{matrix}$

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