$C = \dfrac{x\sqrt{x}+1}{x-1} - \dfrac{x-1}{\sqrt{x}+1}$
$ = \dfrac{x\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x} +1)} - \dfrac{(x-1)(\sqrt{x} - 1)}{(\sqrt{x} -1)(\sqrt{x}+1)}$
$ = \dfrac{x\sqrt{x}+1 - (x\sqrt{x} - \sqrt{x} - x +1)}{(\sqrt{x}-1)(\sqrt{x} +1)}$
$ = \dfrac{\sqrt{x}+x}{(\sqrt{x}-1)(\sqrt{x} +1)}$
$ = \dfrac{\sqrt{x}(\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x} +1)}$
$ = \dfrac{\sqrt{x}}{\sqrt{x}-1}$
Ta có: $x = 2020 + 2\sqrt{2019} = (\sqrt{2019})^{2} + 2\sqrt{2019} + 1 = (\sqrt{2019} + 1)^{2}$
Thay $x$ vào $C$ ta được:
$C = \dfrac{\sqrt{(\sqrt{2019} + 1)^{2}}}{\sqrt{(\sqrt{2019} + 1)^{2}}-1}$
$= \dfrac{\sqrt{2019} + 1}{\sqrt{2019} + 1 -1}$
$= 1 + \dfrac{\sqrt{2019}}{2019}$