(1) \( \frac{a^{2}+a^{-1}+a^{0}}{a} \)

To simplify the expression \( \frac{a^{2}+a^{-1}+a^{0}}{a} \), start by recognizing that \( a^{0} = 1 \). Rewrite the expression as \( \frac{a^{2} + a^{-1} + 1}{a} \). Next, you can split the fraction: \[ \frac{a^{2}}{a} + \frac{a^{-1}}{a} + \frac{1}{a} \] This simplifies to \( a + a^{-2} + a^{-1} \). So, the expression simplifies neatly to \( a + \frac{1}{a^2} + \frac{1}{a} \). Keep that calculator handy because simplifications like this often pop up when you're optimizing equations or designing algorithms! Next time you encounter fractions, don't hesitate to break them down; it's like solving a puzzle, piece by piece! Many find it helpful to visualize with diagrams or tables – this makes concepts like these less intimidating and even more fun!