56. Generalizing problem 55, the members of the math club established that to the numerator of an irreducible fraction, one can add not only the number 2, multiplying the denominator by the same number at the same time. They found the general form of such a number. Find and write it down.
56. Let the desired number be $x$, then $\frac{a+x}{b \cdot x}=\frac{a}{b}$, from which $a+x=a x$ and $x=\frac{a}{a-1}$. This number will be an integer only when $a=2$, and then we have the case considered in problem 55. If, for example, we have $a=5$, then $x=\frac{5}{4}$, and then

$$
\frac{5+\frac{5}{4}}{b \cdot \frac{5}{4}}=\frac{25}{5 \cdot b}=\frac{5}{b}
$$