Evaluating $\frac{2013^3-2\cdot 2013^2\cdot 2014+3\cdot 2013\cdot 2014^2-2014^3+1}{2013\cdot 2014}$ What is the value of $$\frac{2013^3-2\cdot 2013^2\cdot 2014+3\cdot 2013\cdot 2014^2-2014^3+1}{2013\cdot 2014}?$$

What I have tried:
$$\implies\frac{2013^2(2013-2\cdot2014)+2014^2(3\cdot 2013-2014)+1}{2013\cdot 2014}$$
$$\implies\frac{2013^2(-2015)+2014^2(4025)+1}{2013\cdot 2014}$$
I'm not sure what to do next...
Help is appreciated!
Furthermore, if you are nice, could you also help me on this problem(Transferring bases of numbers.) too?
Thanks!
Max0815

Hint
Choose $2013=a$
$$\dfrac{a^3-2a^2(a+1)+3a(a+1)^2-(a+1)^3+1}{a(a+1)}$$
$$=\dfrac{-3a(a+1)+a(a+1)\{3(a+1)-2a\}}{a(a+1)}$$
$$=-3+3+a$$ as $a(a+1)\ne0$
