c is a positive integer. Prove that (6c^3 + 30c) / (3c^2 +15) is an even number.

We aim to factorise the numerator. This would give 6c(c^2 + 5).

We then factorise the denominator. This would give 3(c^2 + 5).

Since (c^2 + 5) is present in both the numerator and denominator, it will cancel.

This leaves us with 6c/3, which simplifies to 2c.

This is an even number because 2 times a positive integer would give an even number.