$12.23 y=\frac{x}{\ln x}$.

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$12.23 y=\frac{x}{\ln x}$.
12.23 The function is defined for $x>0$ and $x \neq 1$. We have

$$
y^{\prime}=\frac{\ln x - x \cdot \frac{1}{x}}{\ln ^{2} x}=\frac{\ln x - 1}{\ln ^{2} x}
$$

Thus, $y^{\prime}=0$ when $\ln x - 1 = 0$, i.e., when $x=e$. Let's construct a table:

| Interval | $(0,1)$ | $(1, e)$ | $e$ | $(e, \infty)$ |
| :---: | :---: | :---: | :---: | :---: |
| $y^{\prime}$ | - | - | 0 | + |
| $y$ | $\searrow$ | $\searrow$ | $\min$ | $\nearrow$ |

Therefore, the function has a minimum at $x=e$. Let's find the value of the function at $x=e$:

$$
y_{\min }=y(e)=\frac{e}{\ln e}=e
$$

Answer: $(e ; e)$ is the point of minimum.