Which method proves (a/b)÷(c/d) = (a·d)/(b·c) better?

[dianzz]

Homework Statement

proof (a/b)/(c/d) = (a/b).(c/d)^-1 = (a.b^-1).(c.d^-1)^-1 = (a.b^-1)(d.c^-1)=(a.d).(b^-1.c^-1) = (a.d).(b.c)^-1 = (a.d)/(b.c)

Homework Equations

The Attempt at a Solution

the other way to proof (a/b).(c/d)^-1 = [(a.b^-1)/(c.d^-1)].(d/d^-1) = (a.d.b^-1)/(c.d.d^-1) =(a.d.b^-1)/c = (a.d)/(b.c)

which one is better proof ?

 

[dianzz]

i mean in more elegant way ..oh yea thanks before ..

 

[drizzle]

Homework Statement

proof (a/b)/(c/d) = (a/b).(c/d)^-1 = (a.b^-1).(c.d^-1)^-1 = (a.b^-1)(d.c^-1)=(a.d).(b^-1.c^-1) = (a.d).(b.c)^-1 = (a.d)/(b.c)

Homework Equations

The Attempt at a Solution

the other way to proof (a/b).(c/d)^-1 = [(a.b^-1)/(c.d^-1)].(d/d^-1) = (a.d.b^-1)/(c.d.d^-1) =(a.d.b^-1)/c = (a.d)/(b.c)

which one is better proof ?

you mean d/d


all works well, though I prefer the first

 

[dianzz]

you mean d/d


all works well, though I prefer the first

yea you right ..thanx for correcting

mm..you prefer the first ,but i dontnow I am suite with the last ..