Question 21
$$
\frac{a}{b} \quad \text{ and } \quad \frac{c}{d}
$$
are called approximately equal if $a, b, c, d$ are positive integers and
$$
\frac{a}{b}-\frac{c}{d}=\frac{1}{b d}
$$
Prove that given two approximately equal fractions, we can multiply the four numerators and denominators by the same positive integer and then add or subtract 1 from each of them so that the resulting fractions are equal.
\frac{a}{b} \quad \text{ and } \quad \frac{c}{d}
$$
are called approximately equal if $a, b, c, d$ are positive integers and
$$
\frac{a}{b}-\frac{c}{d}=\frac{1}{b d}
$$
Prove that given two approximately equal fractions, we can multiply the four numerators and denominators by the same positive integer and then add or subtract 1 from each of them so that the resulting fractions are equal.