2 5/9:х=1 2/21: 2 1/7

To solve the proportion \( \frac{2 \frac{5}{9}}{x} = \frac{1 \frac{2}{21}}{2 \frac{1}{7}} \), we should first convert all the mixed numbers to improper fractions:

1. Convert \(2 \frac{5}{9}\) to an improper fraction: \[ 2 \frac{5}{9} = \frac{2 \times 9 + 5}{9} = \frac{23}{9} \]

2. Convert \(1 \frac{2}{21}\) to an improper fraction: \[ 1 \frac{2}{21} = \frac{1 \times 21 + 2}{21} = \frac{23}{21} \]

3. Convert \(2 \frac{1}{7}\) to an improper fraction: \[ 2 \frac{1}{7} = \frac{2 \times 7 + 1}{7} = \frac{15}{7} \]

Now, substitute these into the proportion: \[ \frac{\frac{23}{9}}{x} = \frac{\frac{23}{21}}{\frac{15}{7}} \]

Simplify the right side of the equation: \[ \frac{23}{21} \div \frac{15}{7} = \frac{23}{21} \times \frac{7}{15} = \frac{23 \times 7}{21 \times 15} = \frac{161}{315} \]

Now we solve for \(x\): \[ \frac{23}{9} \div x = \frac{161}{315} \]

Cross multiply to solve for \(x\): \[ 23 \times 315 = 161 \times 9 \times x \]

\[ 7245 = 1449x \]

Divide both sides by 1449 to solve for \(x\): \[ x = \frac{7245}{1449} = 5 \]

Thus, \(x = 5\).