Let $a$, $b$, $c$, and $d$ be real numbers. Given that $ac=1$, $\dfrac{b+c}{d}$ is undefined, and $abc=d$, which of the following must be true?

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For a fraction to be undefined the denominator must be $0$.

$$\frac{b+c}{d} \text{ is undefined if } d=0$$

If $d=0$,

$$abc = d$$ $$abc=0$$

We are told that $ac=1$. Substituting:

$$abc = 0$$ $$acb =0$$ $$(1)b=0$$ $$b= 0$$