To simplify the expression $a(x+1) + b - (ax + b)$, follow these steps:

1. Expand the terms inside the parentheses:

   • $a(x+1)$ becomes $ax + a$.
   • $-(ax + b)$ becomes $-ax - b$.

   So the expression now looks like: $ax + a + b - ax - b$

2. Combine like terms:

   • Combine the $ax$ terms: $ax - ax = 0$.
   • Combine the constants: $a + b - b = a$.

Thus, the simplified expression is: $a$

Would you like more details on any step, or do you have any questions?

Here are some related questions that might interest you:

1. How do you simplify expressions with multiple parentheses?
2. How do you expand and simplify expressions involving distributive property?
3. How can you simplify expressions with variables on both sides?
4. What are the rules for combining like terms in algebra?
5. How do you handle subtraction of expressions in algebra?

Tip: Always distribute and combine like terms systematically to simplify expressions efficiently!