You have two equations: 1st: [tex]1J=1N*1m[/tex] and 2nd: [tex]1V=\frac{1J}{1C}[/tex]
from the second equation you can extract Joule: [tex]1J=1V*1C[/tex] you compare right side of the equation above to the right side of the 1s equation: [tex]1V*1C=1N*1m[/tex]
then you devide both sides by 1C and by 1m and you get: [tex]\frac{1V}{1m}=\frac{1N}{1C}[/tex]
