Question

(Discrete Mathematics) If m and n are nonzero integers, show that (2m+3n)/5mn is a rational number.

Answer 1

`((2m+3n))/(5mn)=(2)/(5n)+(3)/(5m)` is a rational number for any m and n; nonzero integers.

Explanation:

We have been given that 'm' and 'n' are nonzero integers. We are asked to show that
`((2m+3n))/(5mn)` is a rational number.

We can rewrite our given number as:

`(2m)/(5mn)+(3n)/(5mn)`

Cancelling out common terms:

`(2)/(5n)+(3)/(5m)`

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.