22. (12 points) Given the function
$$
f(x)=\frac{m x-n}{x}-\ln x \quad (m, n \in \mathbf{R}) \text{.}
$$
(1) If the tangent line to the function $f(x)$ at the point $(2, f(2))$ is parallel to the line $x-y=0$, find the value of the real number $n$;
(2) Discuss the maximum value of the function $f(x)$ on the interval $[1,+\infty)$;
(3) If $n=1$, the function $f(x)$ has exactly two zeros $x_{1}, x_{2} \left(0 < x_{1} < x_{2}\right)$. Prove that $x_{1} + x_{2} > 2$.
22. (1) Notice,
$$
f^{\prime}(x)=\frac{n-x}{x^{2}}, f^{\prime}(2)=\frac{n-2}{4} \text {. }
$$

Since the tangent line to the function $f(x)$ at the point $(2, f(2))$ is parallel to the line $x-y=0$, we have,
$$
\frac{n-2}{4}=1 \Rightarrow n=6 \text {. }
$$
(2) It is easy to see that, $f^{\prime}(x)=\frac{n-x}{x^{2}}(x>0)$.

By $f^{\prime}(x)n ; f^{\prime}(x)>0$ when $x<n$, we get
(i) When $n \leqslant 1$, $f(x)$ is monotonically decreasing on the interval $[1,+\infty)$.