432. Split the fraction $\frac{n}{d}$ into two fractions, the denominator $d$ of which is the product of two numbers $a$ and $b$ that have no common divisor $\left(\frac{n}{d}=\frac{58}{77}\right)$.
432. We assume $\frac{n}{d}=\frac{x}{b}+\frac{y}{a}$, from which $a x+b y=n$; for the given case $d=77=11 \cdot 7$, therefore, $a=11$ and $b=7$. We obtain the indeterminate equation $11 x+7 y=58 ; x=7 t-3$; 186
$y=13-11$; under the condition of solving in integers $t=1$, $\boldsymbol{x}=4$ and $y=2$. Therefore, $\frac{53}{77}=\frac{4}{7}+\frac{2}{11}$.