The numerator of a rational number is 3 less than the denominator.

Let, the denominator of the rational number be $\mathrm{x}$.

$\therefore$ The numerator of the rational number will be $\mathrm{x}-3$.

$\therefore$ The rational number $=\frac{\mathrm{x}-3}{\mathrm{x}}$

According to the question,

$\frac{x-3+2}{x+5}=\frac{1}{2}$

or $\frac{\mathrm{x}-1}{\mathrm{x}+5}=\frac{1}{2}$

or $2 \mathrm{x}-2=\mathrm{x}+5$

or $2 \mathrm{x}-\mathrm{x}=5+2$

or $\mathrm{x}=7$

$\therefore$ The rational number $=\frac{7-3}{7}=\frac{4}{7}$