Fraction of pure phase A = fA

Fraction of pure phase B = fB

Since the sum of fractions is always equal to unity (or 1) [sum of fractions constraint], we get:

fA + fB = 1

Mole fraction of a species is the ratio of its molar content to the total amount of moles of all the species in that solution.

Mole fraction of B: fB/(fA + fB) = X0

or, fB = X0 (since the denominator is equal to 1)

This substituting this value of fB in previous equation, we get,

fA = 1-fB = 1-X0.

Thus the final fractions fA and fB are equal to (1-X0) and X0, respectively.

Hope this helps.