c is a positive integer. Prove that (6c^3+30c) / ( 3c^2 +15) is an even number.
Our starting equation (6c3+30c) / ( 3c2 +15) can be factorised by 6c on the top row and 3 on the bottom row so you get 6c(c2+5) / 3(c2+5). Because (c2+5) is on the top and bottom row it can be cancelled out so you have 6c / 3. This can be further simplified as 6c / 3 can be split into 6/3 x c/1 and because 6/3 = 2 this gives us 2 x c/1 = 2 x c = 2c. Therefore the answer will be a multiple of 2, so the answer will be even.
LA
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