$$( \frac{ 8 }{ 17 } \div \frac{ 16 }{ 51 } )+( \frac{ 3 }{ n } \div \frac{ 9 }{ 8 } )= \frac{ 5 }{ 3 }$$
$n=16$
$$\frac{8}{17}\times \frac{51}{16}+\frac{\frac{3}{n}}{\frac{9}{8}}=\frac{5}{3}$$
$$\frac{8\times 51}{17\times 16}+\frac{\frac{3}{n}}{\frac{9}{8}}=\frac{5}{3}$$
$$\frac{408}{272}+\frac{\frac{3}{n}}{\frac{9}{8}}=\frac{5}{3}$$
$$\frac{3}{2}+\frac{\frac{3}{n}}{\frac{9}{8}}=\frac{5}{3}$$
$$\frac{\frac{3}{n}}{\frac{9}{8}}=\frac{5}{3}-\frac{3}{2}$$
$$\frac{\frac{3}{n}}{\frac{9}{8}}=\frac{10}{6}-\frac{9}{6}$$
$$\frac{\frac{3}{n}}{\frac{9}{8}}=\frac{10-9}{6}$$
$$\frac{\frac{3}{n}}{\frac{9}{8}}=\frac{1}{6}$$
$$\frac{3}{n}=\frac{1}{6}\times \frac{9}{8}$$
$$24\times 3=\frac{1}{6}\times \frac{9}{8}\times 24n$$
$$3\times 24=\frac{1}{6}\times \frac{9}{8}\times 24n$$
$$3=\frac{1}{6}\times \frac{9}{8}n$$
$$3=\frac{1\times 9}{6\times 8}n$$
$$3=\frac{9}{48}n$$
$$3=\frac{3}{16}n$$
$$\frac{3}{16}n=3$$
$$n=3\times \frac{16}{3}$$
$$n=16$$
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