Give me 20 other complex algebraic expressions and there solutions

$\frac{x^2 - 4}{x^2 + 4x + 4}$
Solution: $\boxed{\frac{x-2}{x+2}}$

$3(x-2) + 5 = 2x - 1$
Solution: $\boxed{x=0}$

$x^3 - 8$
Solution: $\boxed{(x-2)(x^2+2x+4)}$

$\sqrt{75} - \sqrt{12}$
Solution: $\boxed{3\sqrt{3}}$

$x^2 - 5x + 6 = 0$
Solution: $\boxed{x=2 \text{ or } x=3}$

$\left(\frac{a^2b^{-3}}{a^{-1}b^2}\right)^2$
Solution: $\boxed{\frac{a^6}{b^{10}}}$

$\log_2(x+3) = 4$
Solution: $\boxed{x=13}$

$\frac{1}{x+1} + \frac{1}{x-1}$
Solution: $\boxed{\frac{2x}{x^2-1}}$

$2^{x-1} = 16$
Solution: $\boxed{x=5}$

$2x^2 + 7x + 3$
Solution: $\boxed{(2x+1)(x+3)}$

$\frac{x^2 - 9}{x^2 - 6x + 9} \div \frac{x+3}{x-3}$
Solution: $\boxed{1}$

$\sqrt{2x+1} = 3$
Solution: $\boxed{x=4}$

$(3x-2y)^2 - (3x+2y)^2$
Solution: $\boxed{-24xy}$

$|2x-3| = 7$
Solution: $\boxed{x=5 \text{ or } x=-2}$

$\frac{x^3y^2 - x^2y^3}{x^2y^2}$
Solution: $\boxed{x-y}$

$\frac{x}{x-2} = \frac{3}{x-2} + 1$
Solution: $\boxed{\text{No solution}}$

$\log_3(27x^2) - \log_3(x)$
Solution: $\boxed{3 + \log_3(x)}$

$x+y=5$ and $2x-y=1$
Solution: $\boxed{x=2, y=3}$

$\frac{x^2+x-6}{x^2-4} \cdot \frac{x+2}{x-2}$
Solution: $\boxed{\frac{x+3}{x-2}}$

$e^{2x} - 3e^x + 2 = 0$
Solution: $\boxed{x=0 \text{ or } x=\ln(2)}$