Atrisiniet y=x^n/left(x+1right)^2left(x+2right)^2

$$y = \frac{ { x }^{ n } }{ { \left(x+1 \right) }^{ 2 } { \left(x+2 \right) }^{ 2 } }$$

Atrast n (complex solution)

$$\left\{\begin{matrix}n=\log_{x}\left(y\left(\left(x+1\right)\left(x+2\right)\right)^{2}\right)+\frac{2\pi n_{1}i}{\ln(x)}\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq -2\text{ and }x\neq -1\text{ and }y\neq 0\text{ and }x\neq 1\text{ and }x\neq 0\\n\in \mathrm{C}\text{, }&\left(x=0\text{ and }y=0\right)\text{ or }\left(x=1\text{ and }y=\frac{1}{36}\right)\end{matrix}\right,$$

Atrast n

$$\left\{\begin{matrix}n=\log_{x}\left(y\left(\left(x+1\right)\left(x+2\right)\right)^{2}\right)\text{, }&y>0\text{ and }x\neq 1\text{ and }x>0\\n\in \mathrm{R}\text{, }&x=1\text{ and }y=\frac{1}{36}\\n>0\text{, }&x=0\text{ and }y=0\end{matrix}\right,$$