1. **State the problem:** Simplify the expression $I(x) = \frac{2x^2 + 5x}{x + 1}$. 2. **Formula and rules:** To simplify a rational expression, factor the numerator and denominator if possible, then cancel common factors. 3. **Factor the numerator:** $$2x^2 + 5x = x(2x + 5)$$ 4. **Rewrite the expression:** $$I(x) = \frac{x(2x + 5)}{x + 1}$$ 5. **Check for common factors:** The denominator is $x + 1$, which does not factor further and is not a factor of the numerator. 6. **Conclusion:** No common factors to cancel, so the simplified form is: $$I(x) = \frac{x(2x + 5)}{x + 1}$$ 7. **Domain restriction:** $x \neq -1$ because the denominator cannot be zero. **Final answer:** $$I(x) = \frac{x(2x + 5)}{x + 1}, \quad x \neq -1$$