8 1/3 ÷x=2 1/3 ÷8.1

$8\dfrac{1}{3}\div x = 2\dfrac{1}{3}\div 8.1\\ \dfrac{25}{3}\times 8.1 = \dfrac{7}3 \times x\\ 25 \times 8.1 = 7x\\ x= 25 \times 8.1 \times \dfrac{1}{7}\\x=\frac{405}{14}=28\dfrac{13}{14}$

Solve for x:
25/(3 x) = 0.288066

0.288066 = 70/243:
25/(3 x) = 70/243

Take the reciprocal of both sides:
(3 x)/25 = 243/70

Multiply both sides by 25/3:
Answer: |  x = 405/14=28 + 13/14