Factorial limits $\lim _{x\to \infty }\frac{\left(x!\right)^3\left(3\left(x+1\right)\right)!}{\left(\left(x+1\right)!\right)^3\left(3x\right)!}$ $$\lim _{x\to \infty }\frac{\left(x!\right)^3\left(3\left(x+1\right)\right)!}{\left(\left(x+1\right)!\right)^3\left(3x\right)!}$$
i read this Calculating limit involving factorials.
I don't understand how they eliminate !
The answer is 27.

Hint:
$$(x!/(x+1)!)^3=1/(x+1)^3$$ and  $$(3(x+1)!)/(3x)!=(x+1)(x+2)(x+3)$$
