The expression relating mole fraction of solute in a solution with its molality is where the various symbols have their usual meanings.

Let W₁ and M₁ stand for the solvent's weight and molecular weight, respectively.
Molality $m=\frac{n_2}{W_2}$

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

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