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Let's analyze and solve the given problem step by step.

### Given Expression:
\[
\frac{2xh + h^2 + 7h}{h}
\]

### Step 1: Combine Like Terms
We can factor out \(h\) from the numerator:
\[
\frac{h(2x + h + 7)}{h}
\]

Since \(h\) is in both the numerator and denominator, we can cancel out \(h\):
\[
2x + h + 7
\]

### Final Simplified Expression:
The simplified answer is:
\[
2x + h + 7
\]

So, \( f(x + h) - f(x) = 2x + h + 7 \).

Would you like a detailed explanation or have any questions about this solution?

Here are 5 related questions:
1. How do you factor polynomials?
2. What happens when the numerator and denominator have common factors?
3. How do you simplify rational expressions?
4. What is the difference between combining like terms and factoring?
5. Why is it important to simplify expressions?

**Tip:** Always check for common factors in both the numerator and denominator before canceling terms in fractions.

Combine like terms and simplify the expression \( \frac{2xh + h^2 + 7h}{h} \), then factor and simplify \( f(x + h) - f(x) \).

Learn how to combine like terms, simplify the rational expression \( \frac{2xh + h^2 + 7h}{h} \), and factor the result using common factors. Understand the key concepts behind simplification and factoring, suitable for students in Grades 8-10.

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