Simplify the following expressions: (22025 - 22023) / (22021 - 22019) and (3^(x+4) - 63^(x+1)) / (73^(x+2)).

$$\frac{2^{2025} - 2^{2023}}{2^{2021} - 2^{2019}} = \frac{2^{2023}(2^{2025-2023} - 1)}{2^{2019}(2^{2021-2019} - 1)}$$ $$= \frac{2^{2023}(2^2 - 1)}{2^{2019}(2^2 - 1)}$$

$$= \frac{2^{2023}(4 - 1)}{2^{2019}(4 - 1)}$$ $$= \frac{2^{2023}(3)}{2^{2019}(3)}$$ $$= \frac{2^{2023}}{2^{2019}}$$

$$= 2^{2023 - 2019}$$ $$= 2^4$$ $$= 16$$

The value of the expression is $\boxed{\text{16}}$.

Question 2.2.1
To simplify the expression, we will use exponent rules and factor out common terms.

$$\frac{3^{x+4} - 6 \cdot 3^{x+1}}{7 \cdot 3^{x+2}} = \frac{3^{x+1} \cdot 3^3 - 6 \cdot 3^{x+1}}{7 \cdot 3^{x+2}}$$ $$= \frac{3^{x+1}(3^3 - 6)}{7 \cdot 3^{x+2}}$$

$$= \frac{3^{x+1}(27 - 6)}{7 \cdot 3^{x+1} \cdot 3^1}$$ $$= \frac{3^{x+1}(21)}{7 \cdot 3^{x+1} \cdot 3}$$

$$= \frac{21}{7 \cdot 3}$$ $$= \frac{21}{21}$$ $$= 1$$

The simplified expression is $\boxed{\text{1}}$.

Question 2.2.2
To simplify the expression, we will use the property $\sqrt{A} \times \sqrt{B} = \sqrt{AB}$ and the difference of squares formula $(a+b)(a-b) = a^2 - b^2$.

Let $a=x$ and $b=\sqrt{4x-4}$.

$$= \sqrt{x^2 - (\sqrt{4x-4})^2}$$ $$= \sqrt{x^2 - (4x-4)}$$ $$= \sqrt{x^2 - 4x + 4}$$

$$= \sqrt{(x-2)^2}$$ $$= |x-2|$$

The simplified expression is $\boxed{|x-2|}$.

Question 2.3.1
To solve for $x$, we need to express both sides of the equation with the same base.

$$(\sqrt{x})^2 = 3^2$$ $$x = 9$$

The solution is $\boxed{x=9}$.

Question 2.3.2
To solve for $x$, we will transform the equation into a quadratic form.

Substitute $y$ into the equation.

$$y + \frac{15}{y} = 2$$

$$\Delta = (-2)^2 - 4(1)(15)$$ $$\Delta = 4 - 60$$ $$\Delta = -56$$

Since the discriminant $\Delta < 0$, there are no real solutions for $y$. As $y = 5^x$ must be a positive real number, there are no real solutions for $x$.
The equation has $\boxed{\text{no real solutions}}$.