Simplify and State Restrictions: (x^2-4x-5)/(x^2-3x-10) * (9x+3x^2)/(x^2-9)?

I answered it already, but I need help clarifying something or a few things.

So, the first step is to reduce and factor:

((x+1)(x-5))/((x-5)(x+2)) x (3x(x+3))/((x-3)(x+3))

= (x+1)/(x+2) * ((3x)/(x-3))

Final Answer is:

3x(x+1)/ (x+2)(x-3)

I have a question though about the 3x on the right side of the equation that is left over on the numerator, after the reduction, the equation looks like:

(x+1)/(x+2) * (3x)/(x-3)

I took the 3x and placed it in front of the (x+1) so its 3x(x+1) on the numerator. Is this the correct step to take when there is a co efficient that is left over on the right side?

Thanks in Advance!