How to prove ?
# a/b = c/d = e/f #
# 1/27 ((a+b)/b + (c+d)/d + (e+f)/f)^3 = [(a+b)(c+d)(e+f)]/(bdf) #
We start by expanding the LHS of the equation.
This can be further simplified:
We move to the RHS. Notice that
Indeed, both the LHS and RHS simplify to the same expression, so they must be equivalent.