First, you really need to use parentheses.   What you wrote:  "15xz + 15z/25xyz - 25yz"   means  (15xz) + (15z/25xyz) - (25yz)   and based on what you said the answer was, I'm pretty sure that's not what you meant to write.    You probably meant  (15xz+15z)/(25xyz-25yz).

Regarding your work, you did everything correct up to when you wrote z(3x+3) / yz(5x-5).    Then you mistakenly cancelled the z on the top with the yz on the bottom.   You can only cancel the z on the top with the z on the bottom.   That would leave you with (3x+3) / y(5x-5)  which is the same as the answer since y(5x-5) = 5xy-5y.
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> I made X=1, y=2, and z=3.

You don't really want to do this sort of thing when simplifying expressions, and it appears you didn't end up making use of it.

The problem is that subbing in numbers gets you just a numeric answer, and it might lead you to decide that variables you assigned to be 1 were unimportant as factors, i.e. 3xy + 2x /  5 here would evaluate to be 8/5 so you might decide this could just be 3y+2 / 5.
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