Substitution

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After some calculation I arrive to the following equation $\frac{Dp - D+ I}{D(P-1)}$.

Whichever be the command I use I cannot put it as $\frac{D(p - 1)+ I}{D(P-1)}$ or as $1-\frac{I}{D*(P-1)}$ or $1-\frac{I}{D}\frac{1}{(P-1)}$.

This last equation is the one of interest since I would like to solve $1-\frac{I}{D}\frac{1}{(P-1)}==0$ according to $\frac{D}{I}$.

Is there a way to use solve() acording to $\frac{D}{I}$ ? I have tried to substitue x with a form of substitute()for it, but it was an echec. I understand that substitue a ratio of 2 variables for one is a little bit complex.