let weight of the solvent be w gm and weight of the solution be Wgm

then weight of the solvent=(W-w)gm

 

density D=W/V  (V=volume of the solution)

 

molality m=(w x1000)/(M'x(W-w))

 

this implies, (W-w)=(w x1000)/(M'xm)

 

=> W=w [(1000+M'm)/M'm]

 

now,

molarity M=(w x1000)/(M' x V)

 

=> V=(w x1000)/(MxM')

 

now

D=W/V

=> D=[{(1000+M'm)/M'm}/{1000/MM'}]

 

=> D=[(1000+M'm)xMM'] / [1000x M'm]

 

open the brackets and u'll get-

 

M/m + MM'/1000

 

= M[1/m + M'/1000].......this is ur answer