S5=5x5-(4x4-(3x3-(2x2-1x1)))

S2011=2001x2001-(2000x2000-(1999x1999-(....)))

\(\dfrac{x^2+\sqrt{x}}{x-\sqrt{x}+1}+1-\dfrac{2x+\sqrt{x}}{\sqrt{x}}=\dfrac{\sqrt{x}\left(x\sqrt{x}+1\right)}{x-\sqrt{x}+1}+1-\dfrac{\sqrt{x}\left(2\sqrt{x}+1\right)}{\sqrt{x}}=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{x-\sqrt{x}+1}+1-\left(2\sqrt{x}+1\right)=\sqrt{x}\left(\sqrt{x}+1\right)+1-2\sqrt{x}-1=x+\sqrt{x}+1-2\sqrt{x}-1=x-\sqrt{x}\)

9+9=18

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567432+45678= 613110