[tex]\displaystyle\it\\E(x)=\frac{x^3}{x-1}\bigg(\frac{1}{x^2}-\frac{1}{x^4}\bigg)-\frac{x+3}{x}.\\E(x)=\frac{x^3}{x-1}\bigg(\frac{x^2-1}{x^4}\bigg)-\frac{x+3}{x}.\\E(x)=\frac{x^3(x^2-1)}{x^4(x-1)}-\frac{x+3}{x}.\\E(x)=\frac{x^3(x-1)(x+1)}{x^4(x-1)}-\frac{x+3}{x}.\\E(x)=\frac{x+1}{x}-\frac{x+3}{x}=\frac{x+1-x-3}{x}=-\frac{2}{x},~\forall~x\in\mathbb{R}-\left\{0,1\right\}.[/tex]
