Question about conditional probability when condition involves more than one event

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Suppose $A, B, C$ are events. I seem to not be understanding correctly the concepts of conditional probability when it is conditioned on more than one events. Specifically, how does one express $P(A|B \cup C)$ and $P(A|B \cap C)$ in terms of more simpler (conditioned only on $B$ or $C$) conditional probabilities?