Simplify the expression $\frac{3}{x-2}+\frac{2x+3}{x^2+2x+4}+\frac{-\left(6x+12\right)}{x^3-8}$

$factor\left(121+198x^6+81x^{12}\right)$

$\left(\frac{4}{3} x^2 y^3\right)^3\left(\frac{3}{16x^5}\right)^2$

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

$\sqrt{\frac{x^3-y^3}{x+y}\cdot\frac{x^2+2x\cdot y+y^2}{x^2+xy+y^2}}\frac{x^2-y^2}{4}$

$\log_{5}\left(5^2\right) x^8$

$5\frac{x^2+3x+5}{2x-1}\cdot\frac{2x^2-2x-13}{4x^2-4x+1}$

$factor\left(27x^3+135x^2+225x+125\right)$