To simplify the expression $2x^2 - 3x - x^2 + 3$, we follow these steps:

1. Combine like terms:
   • For the $x^2$ terms: $2x^2 - x^2 = x^2$
   • For the $x$ terms: $-3x$
   • The constant term remains $+3$.

So the simplified expression is:

$x^2 - 3x + 3$

Would you like further explanation on any part of this process?

Here are 5 related questions you can explore:

1. How do you factor $x^2 - 3x + 3$?
2. What is the value of $x$ when $x^2 - 3x + 3 = 0$?
3. How do you graph the quadratic equation $y = x^2 - 3x + 3$?
4. What are the vertex and axis of symmetry for the function $y = x^2 - 3x + 3$?
5. Can you simplify a cubic expression like $x^3 - 2x^2 + x - 1$?

Tip: Always group like terms when simplifying algebraic expressions to make the process clearer.