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.