Упростите выражение: ((x+1)/x)^(-2)*(x^(-2)+2x^(-1)+1).

\[\left( \frac{x + 1}{x} \right)^{- 2} \cdot \left( x^{- 2} + 2x^{- 1} + 1 \right) =\]

\[= \frac{x^{2}\left( x^{- 2} + 2x^{- 1} + 1 \right)}{(x + 1)^{2}} =\]

\[= \frac{x^{- 2 + 2} + 2 \cdot x^{- 1 + 2} + x^{2}}{(x + 1)^{2}} =\]

\[= \frac{1 + 2x + x^{2}}{(x + 1)^{2}} = \frac{(x + 1)^{2}}{(x + 1)^{2}} = 1\]