\[\boxed{\mathbf{167}.}\]
\[1)\ 2x + 1 = \frac{1}{x}\]
\[y = 2x + 1;\]
\[y = \frac{1}{x}.\]
\[x = - 1;\ \ x = 0,5.\]
\[2)\ 1 - x = - \frac{2}{x}\]
\[y = 1 - x;\]
\[y = - \frac{2}{x}.\]
\[x = - 1;\ \ x = 2.\]
\[3)\ x^{2} + 2 = \frac{3}{x}\]
\[y = x^{2} + 2;\]
\[y = \frac{3}{x}.\]
\[x = 1.\]
\[4)\ \sqrt{x + 1} = x^{2} - 1\]
\[y = \sqrt{x + 1};\]
\[y = x^{2} - 1.\]
\[x = - 1;\ \ x = 1,5.\]