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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.

Simplify the expression: y = (sqrt(x) + x) / x^2

Learn how to simplify the expression y = (sqrt(x) + x) / x^2 step by step. This problem involves exponents, square roots, and fraction simplifications. Suitable for students in Grades 9-11.

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