To perform the addition or subtraction and simplify the expression $9 + \frac{x}{x} + 1$, we can follow these steps:

Step 1: Simplify the term $\frac{x}{x}$

• For any non-zero value of $x$, $\frac{x}{x} = 1$.

So, the expression becomes: $9 + 1 + 1$

Step 2: Perform the addition

$9 + 1 + 1 = 11$

Thus, the simplified expression is: $\boxed{11}$

Would you like further explanation on any step, or do you have any other questions?

5 Related Questions:

1. How do we handle undefined expressions like $\frac{x}{x}$ when $x = 0$?
2. What are other common algebraic simplifications involving fractions?
3. How do we simplify more complex expressions with variables and fractions?
4. Can you explain how the distributive property works in algebraic simplifications?
5. How does factoring help in simplifying algebraic expressions?

Tip: Always check for restrictions (like $x \neq 0$ in this case) when simplifying expressions with variables.