Relation between molarity (M) and mole fraction is ___?

Let ‘M’ be the molarity of solution and χA,χB be mole fractions of solvent and solute, respectively.Suppose nA and nB moles of solvent and solute are mixed to form solution.Mass of solution = nA×MA+nB×MBwhere MA and MB are molar masses of solute and solvent, respectively.Vsolution=massdensity=nAMB+nBMBdMolarity, M=No. of moles of solute×1000volume of solution in ml∴M=nB×1000×dnAMB+nBMB  divide both numerator and denominator withnA+nBM=nBnA+nB×1000×dnAmAnA+nB+nBmBnA+nB=χB×1000×dχA.MA+χBMBM=χB×1000×dχA.MA+χBMB