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\(Let x=2014.\\
Exp.=\dfrac{(x^2-2020)*(x^2+4025)*2015}{2011*2013*2016*2017}\\ ~~~~~~\\ ~~\\
(x^2-2020)*(x^2+4025)=\{x^2~-~(x+6)\}*\{x^2~+~(2x-3)\}\\~~~\\
=x^4~+~(x-9)x^2~-~(2x^2+3x-18)\\ ~~\\
{\color{red}{=x^4~+~x^3~-~11x^2~-~9x+18.}}\\~~~\\ ~~\\
2011*2013*2016*2017=(x-3)*(x-1)*(x+2)*(x+3)\\ ~~~\\
=x^4~+~(-3-1+2+3)x^3~+~\{(3-6-9)~+~(-2-3)~+~6\}x^2~+~(-6-18+9+6)x~+~18\\ ~~~\\
{\color{red}{=x^4~+~x^3~-~11x^2~-~9x~+~18.}}\\~~~\\~~~\\
Exp.= \dfrac 1 1*2015=\color {blue}{\Large 2015} . \)
Since I used calculator to know the answer, I used the above solution.