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

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

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

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

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

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

Answered by Oliver B. Maths tutor

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