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9+\frac{1}{0.9+\frac{1}{10}}
Add 9 and 1 to get 10.
9+\frac{1}{\frac{9}{10}+\frac{1}{10}}
Convert decimal number 0.9 to fraction \frac{9}{10}.
9+\frac{1}{\frac{9+1}{10}}
Since \frac{9}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.
9+\frac{1}{\frac{10}{10}}
Add 9 and 1 to get 10.
9+\frac{1}{1}
Divide 10 by 10 to get 1.
9+1
Anything divided by one gives itself.
10
Add 9 and 1 to get 10.