Changing the inertial reference frame to follow a mass in a collision

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1. The problem statement, all variables and given/known data
We could change to inertial reference frame in a collision to follow a mass. But what would the down side be if we did?

2. Relevant equations
Vf1=(M1-M2)/(M1+M2)*Vi1 +2M2/(M1+M2)*Vi2

Vf2=2M1/(M1+M2)*Vi1 +(M1-M2)/(M1+M2)*Vi2

3. The attempt at a solution
This question appears too simple and my teacher doesn't want to even tell me I'm partially right. But it seems that if you followed one mass the final velocity would be higher it actually is, it is higher by the speed of the object that we follow. If you play around with the equation you see that this is true..... i think.
So am I right or wrong. And, if I'm right, what am I missing?
Are you really changing the inertial frame of reference? For instance, my measurement of both velocities could be off if I were in motion. Say one of the masses and I were moving at the same rate, it would appear motionless just as cars do when traveling at the same speed. So what you consider an absolute velocity doesn't really matter, so long as all are in the same inertial frame of reference and the relative velocities are accurate.

In fact all objects could be subject to uniform acceleration--say in free fall and momenta would be still conserved.
This is the actual question
"Discuss how the two equations might be simplified if we choose a different inertial reference frame for some problem under consideration. Explain the potential downside in taking this approach in solving elastic collision problems in one dimension."
Ok I think see what he wants: did you derive the above equations yourself or look them up.

You might try deriving those in 2 different cases: when both masses have non-zero velocities and then again when one mass has an initial velocity of zero. The latter is not too bad, the former derivation is fairly ugly. The drawback may be in forgetting to convert back to the initial frame of reference when computing energy.

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