Rewriting an expression what math operation did my teacher do?

[Femme_physics]

Rewriting an expression...what math operation did my teacher do?

I'm trying to see how did my teacher rewrite this expression in the following manner:

http://imageshack.us/photo/my-images/825/equationnnn.jpg/

What mathametical operation did he do? I really can't see it...

 

[danago]

Have you definitely copied it correctly? If the S² term in the denominator were S²/C then it would seem that he divided the numerator and denominator by RLC.

 

[MathematicalPhysicist]

Simple algebraic manipulation, dividing the numerator by RCL and also the denominator.

He forgot 1/C in the denominator for S^2.

 

[HallsofIvy]

It looks straightforward to me. Initially, there is "SL" in the numerator while after the "operation" there is "S/RC". So the "S" is left alone and we have divided the numerator by 1/LRC. Dividing the denominator by that same 1/LRC gives (RLS^2+ LS+ R)/RLC= S^2/C+ S/RC+ 1/LC, almost what you have. Either your teacher accidently dropped the "C" dividing S^2 or there is some physical reason (you don't say, but I would guess this is an "LRC circuit equation) why that can be done although it does not look likely.

 

[Femme_physics]

You guys are right, I miscopied! It's RLCS^2 and not RLC^2 at the denominator of the first expression..oops. Thank you, though, because saying what mathmatical operation he did cleared it out for me :-) I re-solved it and got the same answer he did!