The given expression is:

$y = \frac{\sqrt{x} + x}{x^2}$

Let's simplify this step by step.

Step 1: Separate the terms

We can split the expression into two parts by separating the numerator: $y = \frac{\sqrt{x}}{x^2} + \frac{x}{x^2}$

Step 2: Simplify each term

1. For the first term: $\frac{\sqrt{x}}{x^2} = \frac{x^{1/2}}{x^2} = x^{1/2 - 2} = x^{-3/2}$

2. For the second term: $\frac{x}{x^2} = \frac{x^1}{x^2} = x^{1-2} = x^{-1}$

Step 3: Combine the results

Now, we can rewrite $y$ as: $y = x^{-3/2} + x^{-1}$

This is the simplified form of the given expression.

Would you like more details or have any further questions? Here are some related questions you might find helpful:

1. How do we differentiate the simplified expression $y = x^{-3/2} + x^{-1}$?
2. What is the domain of the original function?
3. How do we find the critical points of the function $y = \frac{\sqrt{x} + x}{x^2}$?
4. How does the original function behave as $x \to \infty$ and $x \to 0^+$?
5. What happens if you change the power of $x$ in the numerator?

Tip: When simplifying expressions with roots and powers, it's often helpful to convert everything into exponents to make the process smoother.