How do I solve this PDE?

How do I solve the partial differential equaiton

$u_{t} = (u_{x})^{-1}$

subject to the conditions $u(t,x) \geq 0$ and $u(0,0) = $0. Use the separation Ansatz $u(t,x) = f(t)g(x)$.

The inverse in confusing me

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