1. **State the problem:** Simplify the expression $\frac{\sqrt{3}}{\sqrt{3}}$. 2. **Formula and rules:** When dividing two identical non-zero numbers, the result is 1. Also, $\frac{\sqrt{a}}{\sqrt{a}} = \sqrt{\frac{a}{a}} = \sqrt{1} = 1$. 3. **Intermediate work:** $$\frac{\sqrt{3}}{\sqrt{3}} = \sqrt{\frac{3}{3}}$$ 4. Simplify the fraction inside the square root: $$\sqrt{\cancel{\frac{3}{\cancel{3}}}} = \sqrt{1}$$ 5. Evaluate the square root: $$\sqrt{1} = 1$$ 6. **Final answer:** The simplified value of $\frac{\sqrt{3}}{\sqrt{3}}$ is **1**.