Monotonic Transformation Clarification

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So I understand that a monotonic transformation preserves the order of a function, but I was wondering: could you perform a transformation by multiplying by a variable?

For example the formula:

U = (XY) - (XY/(Z+1))

Is it an acceptable monotonic transformation to multiply the whole function by (Z+1) [assuming X,Y,Z > 0]? I can't see any reason why not, but I can't find a definite answer.

Thanks.
 
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