Is the Relativistic Law for Adding Velocities Associative?

[NeroBlade]

Hey folks I've been having trouble solving this assignment and I'm not sure whether my solutions is correct or in the right direction.
The one question just need help doing the fraction rearranging to prove that the function is associative.

1. The Relativistic Law for adding velocities is v1 + v2 = (v1 + v2) / (1+((v1*v2)/c^2)) Show that:

Law is associative

I've thought of using (v1 + v2) + v3 = v1 + (v2 + v3) where

(v1 + v2) + v3 = ((v1 + v2)/(1 + (v1*v2/c^2)) + v3) / (1 + (((v1v2)/c^2)*v3) / c^2)

and

v1 + (v2 + v3) = ((v2 + v3)/(1 + (v2*v3/c^2)) + v1) / (1 + (((v2v3)/c^2)*v1) / c^2)

At this point I am stuck in regards of algebraically solving these two fractions.
Could any of you lend me a hand for this problem?

2.

v + c = c

I'm presume that you use one of the addition or multiplication axioms where the you either make v a neutral element
where you get to the point that v + c - c = 0 and v = 0 therefore v + c = 0 + c = c.

3.

If v1,v2 < c then v1 + v2 < c
For this one I've used the Relativistic Law and simulated what would happen if v1,v2 > c
(which is impossible as c is suppose to be the "Ultimate Velocity")
and work out c after for example v1 = 4, v2 = 5 and c = 2 and (v1 + v2)

How am I doing for these proofs are these right? If not what is missing?

Cheers

 

[Delphi51]

Multiply both expressions by their common denominator
c²(v1v2+c²)(v2v3+c²) to clear all the fractions. It will be messy, but possible, to see if the numerators are equal by expanding them out and collecting like terms. Hard to believe they will be equal!