# Can't Rearrange this equation ?

Can't Rearrange this equation!!!!!!???????

## Homework Statement

I need to substitute one equation into another and rearrange for one term. I can't get the right answer!

## Homework Equations

I've had to attach the equations as pictures im afraid, here they are.

The equation to be substituted-http://i423.photobucket.com/albums/pp315/skaboy607/Tobesubstituted.png [Broken]

Main Equation-http://i423.photobucket.com/albums/pp315/skaboy607/MainEquation.png [Broken]

What I cant get!-http://i423.photobucket.com/albums/pp315/skaboy607/FinalEqthatIcantget.png [Broken]

## The Attempt at a Solution

I have a few extra terms when I rearrange, it is driving me mad!

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Make your life easier by writing a=ms^2+Bs+K and c=Bs+K. Also write X instead of X(s) and Y instead of Y(s). Note X=aY/c. Simplify as much as you can. Then substitute a=ms^2+c and simplify some more. It works out.

ok, so far I using your easier notation I have U=cX-cY+Ms^2X, then with substitution, U=caY/c-cY+Ms^2aY/c.

Is this what you meant? Im confused now with when to put a=ms^2+c.

Thanks

You're doing it backwards from the way I did it.

First I rewrote "main equation" as U(s) = etc. Call this "new main equation."

Then I used the easier notation in "tobesubstituted", then substituted into "new main equation." Then I simplified, etc.

From time to time I looked at the goal "FinalEqthatIcantget" but I didn't start with it.

Ok so starting from scratch, my rearranged 'main equation' looks like U=Ms^2X+kX-kY+bsX-bsY. Then Substituting in the easier notationed 'tobesubstitued' I have:

U=Ms^2aY/c+kaY/c-ky+bsaY/c-bsY.

This along the right lines?

Now you've got it! It won't be long now!

I can't simplify that any further so shall I replace my values for a and c in now, then simplify?

Thanks

You've got fractions. Deal with that first.

ok.....do you mean multiply both sides by c to cancel it out? I tried without getting rid of the fractions, and was stuck with the same terms again as before that I cant get rid of. This are '2kbs', '(bs)^2', 'k' and 'k^2'. If it helps this is the equation where I am at.

U=(Mms^4+Mbs^3+Mks^2+kms^2+kbs+k^2-k+mbs^3+(bs)^2+kbs-bs)Y/c

Sorry if im being stupid!

Aha! Common denominator problem (or similar).

Early on, you should have written Y=cY/c.

erm..........i'm lost, where should that have been? Wouldn't the c's cancel to leave Y=Y anyway?

Ok so starting from scratch, my rearranged 'main equation' looks like U=Ms^2X+kX-kY+bsX-bsY. Then Substituting in the easier notationed 'tobesubstitued' I have:

U=Ms^2aY/c+kaY/c-ky+bsaY/c-bsY.

This along the right lines?
Look at right hand side. Get the common denominator here. Three terms have denominator c, but two don't.

Thanks very much for your help! Sorted it!