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Let's break down the given expression and simplify it as a single fraction.

The expression is:

\[
\frac{x}{y^2} + x
\]

To combine these terms, we need a common denominator. The first term already has a denominator of \( y^2 \), while the second term \( x \) can be rewritten as:

\[
x = \frac{x \cdot y^2}{y^2}
\]

Now, the expression becomes:

\[
\frac{x}{y^2} + \frac{x \cdot y^2}{y^2}
\]

Since both terms now have the same denominator, we can combine them:

\[
\frac{x + x \cdot y^2}{y^2}
\]

This simplifies further as:

\[
\frac{x(1 + y^2)}{y^2}
\]

Thus, the simplified expression as a single fraction is:

\[
\boxed{\frac{x(1 + y^2)}{y^2}}
\]

Would you like more details on any step? 

Here are some related questions for further practice:

1. How do you simplify algebraic fractions with multiple terms in the numerator?
2. What is the process of finding a common denominator in algebraic expressions?
3. How do you factor common terms out of expressions?
4. How would you handle a subtraction problem with fractions like this?
5. Can you simplify the result further under specific conditions for \( x \) and \( y \)?

**Tip:** Always look for a common denominator when adding or subtracting fractions to ensure you can combine them properly.

Perform the operation and express your answer as a single fraction in simplest form: \( \frac{x}{y^2} + x \)

Learn how to simplify the algebraic expression \( \frac{x}{y^2} + x \) by finding a common denominator and combining terms. This step-by-step guide covers essential algebraic concepts for students in Grades 7-9.

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