Find \( x \) if: \( \quad x+\frac{1}{x}=\frac{x^{2}+1}{x} \)

To solve the equation \( x + \frac{1}{x} = \frac{x^2 + 1}{x} \), we start by simplifying the right-hand side. We can rewrite the right-hand side: \[ \frac{x^2 + 1}{x} = \frac{x^2}{x} + \frac{1}{x} = x + \frac{1}{x} \] Now, we see that both sides of the equation are equal: \[ x + \frac{1}{x} = x + \frac{1}{x} \] Since both sides are the same, this means the equation is an identity and holds true for all \( x \) in the domain where \( x \neq 0 \). Thus, the solution is: \[ \text{All } x \text{ such that } x \neq 0. \]