How can I simplify this factorial expression?

[Flappy]

Homework Statement

$$\frac{(kn)!}{(kn+k)!}$$

I was thinking:

(kn)! = 1*2*3...(kn)
(kn+k)! = 1*2*3...(kn)(kn+k)

and I would be left with 1/kn+k

But my book has the answer as:
$$\frac{1}{(kn+k)(kn+k-1)...(kn+1)}$$

How can I arrive to that?

 

[mutton]

There are k numbers between kn and kn + k, not just one.