To simplify the given expression $\frac{x^3 + x^2}{x}$:

Step 1: Split the terms in the numerator

$\frac{x^3 + x^2}{x} = \frac{x^3}{x} + \frac{x^2}{x}.$

Step 2: Simplify each term

• $\frac{x^3}{x} = x^{3-1} = x^2$,
• $\frac{x^2}{x} = x^{2-1} = x$.

Step 3: Combine the simplified terms

$x^2 + x.$

Final Answer:

$x^2 + x$

Let me know if you have questions or need further clarification!

Here are five related questions for deeper understanding:

1. How do exponents work when dividing powers of the same base?
2. How would the expression simplify if the denominator was $x^2$ instead of $x$?
3. Can this expression be factored further, and if so, how?
4. What would happen if $x = 0$? Is the expression still valid?
5. How can this simplification be applied in solving equations?

Tip: Always check for common factors in numerator and denominator to simplify expressions easily!