$$\frac { 1 } { 4 \frac { 2 } { 7 } } + \frac { 1 } { 3 \frac { 11 } { 13 } } + \frac { 1 } { \frac { 5 } { 9 } }$$
$\frac{172}{75}\approx 2.293333333$
$$\frac{7}{4\times 7+2}+\frac{1}{\frac{3\times 13+11}{13}}+\frac{1}{\frac{5}{9}}$$
$$\frac{7}{28+2}+\frac{1}{\frac{3\times 13+11}{13}}+\frac{1}{\frac{5}{9}}$$
$$\frac{7}{30}+\frac{1}{\frac{3\times 13+11}{13}}+\frac{1}{\frac{5}{9}}$$
$$\frac{7}{30}+\frac{13}{3\times 13+11}+\frac{1}{\frac{5}{9}}$$
$$\frac{7}{30}+\frac{13}{39+11}+\frac{1}{\frac{5}{9}}$$
$$\frac{7}{30}+\frac{13}{50}+\frac{1}{\frac{5}{9}}$$
$$\frac{35}{150}+\frac{39}{150}+\frac{1}{\frac{5}{9}}$$
$$\frac{35+39}{150}+\frac{1}{\frac{5}{9}}$$
$$\frac{74}{150}+\frac{1}{\frac{5}{9}}$$
$$\frac{37}{75}+\frac{1}{\frac{5}{9}}$$
$$\frac{37}{75}+1\times \frac{9}{5}$$
$$\frac{37}{75}+\frac{9}{5}$$
$$\frac{37}{75}+\frac{135}{75}$$
$$\frac{37+135}{75}$$
$$\frac{172}{75}$$
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$\frac{2 ^ {2} \cdot 43}{3 \cdot 5 ^ {2}} = 2\frac{22}{75} = 2.2933333333333334$
