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If $A$ and $B$ are positive constants, show that $\frac{A}{x-1} + \frac{B}{x-2}$ has a solution on $(1,2)$

If $A$ and $B$ are positive constants, show that $$\frac{A}{x-1} + \frac{B}{x-2}$$ has a solution on $(1,2)$.

Please, support your answers with rigorous proof.