To simplify the expression \(\frac{x^2 + 3x + 2}{x + 1}\), we first factor the numerator.
The expression in the numerator is a quadratic expression: \(x^2 + 3x + 2\). We can factor it as follows:
\[ x^2 + 3x + 2 = (x + 1)(x + 2) \]
Now we can rewrite the original expression:
\[ \frac{x^2 + 3x + 2}{x + 1} = \frac{(x + 1)(x + 2)}{x + 1} \]
Assuming \(x + 1 \neq 0\) (which means \(x \neq -1\)), we can cancel \(x + 1\) from the numerator and the denominator:
\[ = x + 2 \]
Thus, the simplified expression is:
\[ x + 2 \]
Among the options you provided, the correct one is:
- \(x + 2\)