[tex]E(x)=(1+ \frac{2-x}{x+1}) : \frac{x-1}{(2x+1) ^{2}-(x+2) ^{2} } [/tex]
[tex]E(x)=(\frac{x+1+2-x}{x+1}) * \frac{(2x+1) ^{2}-(x+2) ^{2} }{x-1} [/tex]
[tex]E(x)=(\frac{3}{x+1}) * \frac{(2x+1-x-2) (2x+1+x+2)}{x-1}[/tex]
[tex]E(x)=(\frac{3}{x+1}) * \frac{(x-1) (3x+3)}{x-1}[/tex]
[tex]E(x)=\frac{3}{(x+1)} * \frac{3(x-1) (x+1)}{x-1}[/tex]
[tex]E(x)=9[/tex]