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Math·Advanced Math·Nonlinear functions

hard

The function $g$ is defined by $g(x)=\frac{x^2-x-a}{x^2-x-b}$, where $a$ and $b$ are constants. In the $xy$-plane, the graph of $y=g(x)$ passes through the point $(0,43)$, and $g(-43)=0$. What is the value of $b$?

A

44

B

43

C

-43

D

-44