Question

Let x and y be nonzero rational numbers. prove that 5x+2y/3y is rational number

Answer 1

Answer:

5x+2y/3y is a rational number because 2/3 is in the form of p/q

Answer 2

Proof of 5x+2y/3y is a rational number

Given:

x and y be nonzero rational numbers.

To Find:

Proof of 5x+2y/3y being a rational number.

Solution:

We need to understand a few concepts before proceeding to the solution.

A rational number is a number that can be expressed as a ratio of two numbers, where the denominator is always non-zero.

The sum of two rational numbers is always rational.

The product of rational numbers is rational.

Now,

2y/3y = 2/3, is a rational number since it is a fraction where the denominator is non-zero.

Since x is a rational number, so 5x is also a rational number as it can be written as a fraction with a non-zero denominator.

Now, 5x+2y/3y, which is essentially the sum of two rational numbers, is also rational.

Hence, we have proved that 5x+2y/3y is a rational number.

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