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\frac{1}{\frac{4}{144}+\frac{3}{144}}
Least common multiple of 36 and 48 is 144. Convert \frac{1}{36} and \frac{1}{48} to fractions with denominator 144.
\frac{1}{\frac{4+3}{144}}
Since \frac{4}{144} and \frac{3}{144} have the same denominator, add them by adding their numerators.
\frac{1}{\frac{7}{144}}
Add 4 and 3 to get 7.
1\times \frac{144}{7}
Divide 1 by \frac{7}{144} by multiplying 1 by the reciprocal of \frac{7}{144}.
\frac{144}{7}
Multiply 1 and \frac{144}{7} to get \frac{144}{7}.