Polynomial Division puzzler(well to me anyway :P )

[ramstin]

O.K I factored and reduced an equation I am doing down to (s+5t)/(t-s)

I could not figure it out so I went to webmath and used a calculator to find out the answer so I could reverse solve the problem. The answer is 1 according to webmath. Any hints on how to get started on this because I do not see how you can get rid of the 5?

 

[Plastic Photon]

O.K I factored and reduced an equation I am doing down to (s+5t)/(t-s)

I could not figure it out so I went to webmath and used a calculator to find out the answer so I could reverse solve the problem. The answer is 1 according to webmath. Any hints on how to get started on this because I do not see how you can get rid of the 5?

If it is an equation, what is the remaining part of the equation? How did you factor what you have so far?

 

[Hurkyl]

There's a very easy way to prove (s + 5t) / (t - s) is not identically equal to 1. (I'll give you time to figure this one out -- and I advise doing so, it's a widely useful but overlooked technique)


Have you tried going through the problem a second time? I find that I rarely make the same mistake twice. So when I'm not completely confident in my arithmetic, I will often do the same problem twice from scratch (and in different ways, if possible) to check myself. If I get a mismatch, I can often track down exactly what I did wrong.


But finally, I can't possibly figure out what you've done wrong unless you showed your work.

 

[ramstin]

O.k. Here goes. The equation is
20s^2+9st+t^2 2s^2-7st+3t^2 5s^2+6st+t^2
-------------- * --------------- * --------------
5s^2-14st-3t^2 t^2+3st-4s^2 10s^2-3st-t^2


factored out to

(5s+t)(4s+t) (2s-t)(s-3t) (5s+t)(s+5t)
------------*-----------*-------------
(5s+t)(s-3t) (t-s)(t+4s) (5s+t)(2s-t)

reduced to
(s+5t)/(t-s)
from this point I am stuck.

 

[assyrian_77]

The numerator in your last fraction: $5s^2+6st+t^2\neq(5s+t)(s+5t)$.

 

[ramstin]

I re did the equation and ended up with (s+t)/(s-t). Thanks everyone.

 

[HallsofIvy]

So far you haven't shown us any equation. An equation has to have a "= " somewhere in it!

And (s+t)/(s-t) still isn't equal to 1!

 

[ramstin]

Sorry It was perform the indicated operation. Not solve the equation. Honestly i did not know an equation had to have a = . The instructor at the community college I am going to never spent any time on terms.

 

[ramstin]

As for the 1 thing. I think the calculator on webmath is messed up. It said (s+t)/(s-t) =1 But my calculator says in doing so you would have to divide by zero which cannot be done.