Is there a solution (root) to $(1-x)^{-2}$

Question

I have (via Pollaczek-Khintchine formula): $$N=\frac{U}{1-U}$$ Now, when I plot this I can see points of inflection, but I want to show where these are algebraically. But is there a solution to $\frac{1}{(1-U)^2}$ or have I made some mistake along the way here? ($U < 1$ as per the equilibrium condition.)

Answer 1

A fraction $\frac{a}{b}$ is zero if and only if $a=0$ while $b\neq 0$. You have a fraction $\frac{1}{(1-U)^2}$, which can never satisfy the above conditions, thus it is nonzero for every $U$. No root exists.