Checking simplified algebraic expressions (the -3 test)

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".

The best check I have thought of I call the -3 check. You plug in the
number -3 into the unsimplfied expression and the simplified
expression and see if you get the same answer. This technique is not
perfect. Sometime you will get the same answer even if the expressions
are not equivalent such as -3x and x^2 and the test blows up for
expressions like 1/(x+3). Still these problems come up seldomly.

-3 is the smallest and easiest to use number that rarely gives a false
check.

0 fails in multiplication x=2x
1 fails in exponentiation x=x^2
2 has some weird properties x+x = x*x = x^x
3 has a problem with abs(x) = x and some other minor ones

-3 distinguishes all the above situations and is easier to computer
than larger numbers.

So, I want to get your opinion on this test and ask if you can think
of anything better. I encourage my students to review their
calculations but many times they will make the same mistake more than
once if they don't know that their answer is wrong. Remember, in
general I am teaching this to 8th and 9th graders. They are not very
sophisticated or abtract thinkers yet and thier ability to keep track
of multiple things is quite limited.