Fraction Simplification: Solving Equations with Constants C, L, and R

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jkface
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I have the following two equations

5bCv09x.png

3Eq3tTM.png


C, L, and R are all constants.

I need to somehow get the above two equations and get it to look like this:

ieBherg.png


But I can't get mine to look that nice. I have V1(s) = V2(s)(1+sCR) and I substituded it into equation 1 and it ends up looking messy. Any help would be appreciated.
 

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i(s) = V2(s)(1+sCR) / sL + (V2(s)(1+sCR) - V2(s)) / R
i(s) = V2(s)( (1+sCR) / sL + sCR / R)
V2(s) = i(s) (sL / (1+sCR) + 1 / sC) = i(s) ((s^2 * LC + 1 + sCR) / sC(1+sCR))
V2(s) = i(s) ((s^2 * LC + 1 + sCR) / (sC+s^2 * C^2 * R))

this is obviously not what I'm supposed to have.