1. **State the problem:** Simplify the expression $$2\sqrt{t} + \frac{2t + 1}{2\sqrt{t}}$$ and verify the given simplifications. 2. **Recall the rules:** - When adding terms, they must have the same denominator or be like terms. - Simplify fractions by combining numerators over a common denominator. - Use the property $$\sqrt{t} \cdot \sqrt{t} = t$$. 3. **Rewrite the first term with a common denominator:** $$2\sqrt{t} = \frac{2\sqrt{t} \cdot 2\sqrt{t}}{2\sqrt{t}} = \frac{4t}{2\sqrt{t}}$$ 4. **Add the two fractions:** $$\frac{4t}{2\sqrt{t}} + \frac{2t + 1}{2\sqrt{t}} = \frac{4t + 2t + 1}{2\sqrt{t}}$$ 5. **Combine like terms in the numerator:** $$4t + 2t + 1 = 6t + 1$$ 6. **Final simplified expression:** $$\frac{6t + 1}{2\sqrt{t}}$$ **Answer:** The expression simplifies to $$\frac{6t + 1}{2\sqrt{t}}$$ as given.