About algebra?

sqr[(r(r^2-3))^2-4]/(r^2-1)

=

sqr[(r^4-6r^2+9)r^2-4]/(r^2-1)

=

sqr[r^6-6r^4+9r^2-4]/(r^2-1)

=

sqr[(r^2-1)(r^4-5r^2+4)]/(r^2-1)

=

sqr[(r^2-1)(r^2-4)(r^2-1)]/(r^2-1)

=

sqr[(r^2-4)(r^2-1)^2]/(r^2-1)

=

(r^2-1)sqr(r^2-4)/r^2-1)

=

sqr(r^2-4)

This proves that my previous result in another problem

x+y+z=

(3/2){r+/-sqr[(r(r^2-3))^2-4]/(r^2-1)} is exactly=

(3/2)[r+/-sqr(r^2-4)]

That is what I actually want.

Stars are awarded to those who

successfully solves the problem.

What is strange is that you're a level 7 here and you even solve much much harder problems like differential equations and calculus. Yet you're asking to solve a very easy algebra question?

Anw, hint: Square both sides. ]

So, is it true?

Or, can you find a counterexample?