You are entirely correct, and I value your quick reply. I am uncertain how I failed to recognize this (obvious) fact; I must have been fatigued while addressing this equation.
I have corrected this post and opened a new query [1] to explore how to simplify the output further, specifically why it is not presented in its simplest form and if there is a way to enforce maximum algebraic reduction.
[1] Achieving Maximum Algebraic Simplification in Symbolic Computation