The sum of two natural numbers is $21$ and the sum of their squares is $233$. Find the numbers.

The difference of squares of two natural numbers is $45$. The square of the smaller number is four times the larger number. Find the numbers.

The numerator of a fraction is one less than its denominator. If $3$ is added to each of the numerator and denominator, the fraction is increased by $\frac{3}{28}$: find the fraction. $28$