Re: Checking simplified algebraic expressions (the -3 test)

On May 3, 8:57=A0pm, "michalc...@[EMAIL PROTECTED]
" <michalc...@[EMAIL PROTECTED]
> wrote:
> I tutor a lot of algebra and as you know there are three basic types
> of problems that algebra students are given. The ones that say
> "Solve", "Factor" and the ones that say "Simplify".
>
> Solve you check by plugging the answers back in.
>
> Factor you check by multiplying things back together.
>
> Simplify... Well neither my students nor I were ever taught a reliable
> and simple check for simplified expressions. Example "Simplify (x^2
> -1) / (x+1)" this becomes "x-1".

Which, of course, is just wrong.  If  x=3D-1,  then the quotient is
undefined,
but the simplification equals -2.  The correct answer must state this
exception.  Which then begs the question:

Is  (x^2-1)/(x+1)  "simpler"   than   "x-1,   if  x !=3D-1,  and
undefined if x =3D -1"?

I have discussed this issue before. There is no clear canonical
definition of what
makes one algebraic expression "simpler" than another.  Therefore,
from a strict,
well-disciplined mathematical point of view, such questions are
meaningless.