Can't Rearrange this equation ?

[skaboy607]

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 I am afraid, here they are.

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

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

What I can't get!-http://i423.photobucket.com/albums/pp315/skaboy607/FinalEqthatIcantget.png

The Attempt at a Solution

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

Thanks for your help.

 

[Billy Bob]

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.

 

[skaboy607]

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? I am confused now with when to put a=ms^2+c.

Thanks

 

[Billy Bob]

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.

 

[skaboy607]

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?

 

[Billy Bob]

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

 

[skaboy607]

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

Thanks

 

[Billy Bob]

You've got fractions. Deal with that first.

 

[skaboy607]

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 can't 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 I am being stupid!

 

[Billy Bob]

Aha! Common denominator problem (or similar).

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

 

[skaboy607]

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

 

[Billy Bob]

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.

 

[skaboy607]

Thanks very much for your help! Sorted it!