^{55}Recall from algebra that we may perform any arithmetic operation we wish to any equation, so long as we apply that
operation equally to both sides of the equation. Dividing one equation by another equation obeys this principle,
because both sides of the second equation are equal. In other words, we could divide both sides of the first
equation by P_{A}V _{A} (although that would not give us the solution we are looking for), but dividing the left side
by P_{A}V _{A} and the right side by nRT_{A} is really doing the same thing, since nRT_{A} is identical in value to
P_{A}V _{A}.