1. **State the problem:** Simplify the expression $\frac{x^2}{x^2+x}$. 2. **Identify the formula and rules:** To simplify a rational expression, factor numerator and denominator and cancel common factors. 3. **Factor the denominator:** $$x^2 + x = x(x + 1)$$ 4. **Rewrite the expression:** $$\frac{x^2}{x(x + 1)}$$ 5. **Factor the numerator:** $$x^2 = x \cdot x$$ 6. **Rewrite with factored numerator:** $$\frac{x \cdot x}{x(x + 1)}$$ 7. **Cancel common factor $x$:** $$\frac{\cancel{x} \cdot x}{\cancel{x}(x + 1)} = \frac{x}{x + 1}$$ 8. **State the simplified expression:** $$\frac{x}{x + 1}$$ 9. **Note domain restrictions:** $x \neq 0$ and $x \neq -1$ to avoid division by zero. **Final answer:** $$\frac{x}{x + 1}$$