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\frac{4\times \frac{\frac{2}{4}+\frac{1}{4}}{1}}{\frac{1^{2}+2^{2}}{3^{2}}}
Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.
\frac{4\times \frac{\frac{2+1}{4}}{1}}{\frac{1^{2}+2^{2}}{3^{2}}}
Since \frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.
\frac{4\times \frac{\frac{3}{4}}{1}}{\frac{1^{2}+2^{2}}{3^{2}}}
Add 2 and 1 to get 3.
\frac{4\times \frac{3}{4}}{\frac{1^{2}+2^{2}}{3^{2}}}
Anything divided by one gives itself.
\frac{3}{\frac{1^{2}+2^{2}}{3^{2}}}
Cancel out 4 and 4.
\frac{3}{\frac{1+2^{2}}{3^{2}}}
Calculate 1 to the power of 2 and get 1.
\frac{3}{\frac{1+4}{3^{2}}}
Calculate 2 to the power of 2 and get 4.
\frac{3}{\frac{5}{3^{2}}}
Add 1 and 4 to get 5.
\frac{3}{\frac{5}{9}}
Calculate 3 to the power of 2 and get 9.
3\times \frac{9}{5}
Divide 3 by \frac{5}{9} by multiplying 3 by the reciprocal of \frac{5}{9}.
\frac{3\times 9}{5}
Express 3\times \frac{9}{5} as a single fraction.
\frac{27}{5}
Multiply 3 and 9 to get 27.