The molality (m) of a solution in terms of mole fractions of solvent (x₁)  and solute (x₂) is given by the expression, where (M₁) is the molar mass of the solvent.

Let W₁ and M₁ stand for the solvent's weight and molecular weight, respectively.
Molality $\mathrm{m}=\frac{{\mathrm{n}}_2}{{\mathrm{W}}_2}$, Therefore,

${\mathrm{n}}_2={\mathrm{mW}}_1$

${\mathrm{x}}_2=\frac{{\mathrm{n}}_2}{{\mathrm{n}}_1+{\mathrm{n}}_2}=\frac{{\mathrm{mW}}_1}{\frac{{\mathrm{W}}_1}{{\mathrm{M}}_1}+{\mathrm{mW}}_1}=\frac{{\mathrm{mM}}_1}{1+{\mathrm{mM}}_1}$

Now,  mole fractions of solvent (x₁) is,

${\mathrm{x}}_1=\frac{1}{1+{\mathrm{mM}}_1}$

Thus,

$m=\frac{x_2}{x_1{M}_1}$