Simplify the expression $\frac{\frac{\left(3x^{\left(n+1\right)}\right)^2}{x^{2\left(n+1\right)}}x^{-n}}{\left(x^{-n}\right)^3}$

$\frac{\frac{3x-6}{x^2+21x+54}}{\frac{40x^2}{x^2+6x+9}}$

$\frac{x^5+\left(2\cdot \sqrt{3}+2\right) x^3+2\cdot \sqrt{2}+7}{x-\sqrt{2}+1}$

$\frac{m^3n\sqrt{x}}{\left(2^4 m^7 n^6\cdot x\right)^{\frac{1}{5}}}$

$\frac{x^4-\frac{4}{3} x^3-2x^2-\frac{4}{3}\cdot x+1}{x-2}$

$\frac{4x^2+12y\cdot x+9y^2}{3y+2x}$

$\frac{4x^2+12y\cdot x+9y^2}{3y+2x}$

$\frac{\frac{x^2-16}{x-1}}{\frac{x^2+6x+8}{x^2+2x-3}}$