Why does (A'+ AC) = (A'+C)?

Question

Why does (A'+ AC) = (A'+C)?

I can understand this via a truth table, but I cannot see why this works in boolean algebra. Conceptually I understand that A doesn't matter, but I can not seem to prove this. Can someone lend some advice?

Answer 1

$$A'+AC=A'(1+C)+AC=A'+(A'+A)C=A'+C$$

Answer 2

In general, in boolean algebra we also have $X+YZ=(X+Y)(X+Z)$.