Question: top-center: a horizontal fraction with numerator $2 + 2\sqrt{5}$ and denominator $2$
a
$\frac{2 + 2\sqrt{5}}{2}$
Can you please help me simplify this and explain it please
1. **State the problem:** Simplify the expression $$\frac{2 + 2\sqrt{5}}{2}$$.
2. **Formula and rules:** When simplifying a fraction where the numerator is a sum, you can split the fraction into the sum of two fractions:
$$\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$$
3. **Apply the rule:**
$$\frac{2 + 2\sqrt{5}}{2} = \frac{2}{2} + \frac{2\sqrt{5}}{2}$$
4. **Simplify each term:**
$$\frac{2}{2} = 1$$
For the second term, divide numerator and denominator by 2:
$$\frac{2\sqrt{5}}{2} = \cancel{\frac{2}{2}}\sqrt{5} = 1 \times \sqrt{5} = \sqrt{5}$$
5. **Combine the simplified terms:**
$$1 + \sqrt{5}$$
**Final answer:** $$\boxed{1 + \sqrt{5}}$$
This means the original fraction simplifies neatly to $1 + \sqrt{5}$, which is easier to understand and use in further calculations.