Answer:
[tex]\frac{(2m+3n)}{5mn}=\frac{2}{5n}+\frac{3}{5m}[/tex] is a rational number for any m and n; nonzero integers.
Step-by-step explanation:
We have been given that 'm' and 'n' are nonzero integers. We are asked to show that [tex]\frac{(2m+3n)}{5mn}[/tex] is a rational number.
We can rewrite our given number as:
[tex]\frac{2m}{5mn}+\frac{3n}{5mn}[/tex]
Cancelling out common terms:
[tex]\frac{2}{5n}+\frac{3}{5m}[/tex]
Since 'm' and 'n' are nonzero integers, so each part will be a rational number.
We know that sum of two rational numbers is always rational, therefore, our given number is a rational number.
