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Aus Online Mathematik Brückenkurs 1

The fraction can be further simplified if it is possible to factorize and eliminate common factors from the numerator and denominator. Both numerator and denominator are already factorized to a certain extent, but we can go further with the numerator and break it up into linear factors by using the conjugate rule

3x2−12x2−1=3(x2−4)=3(x+2)(x−2)=(x+1)(x−1).

The whole expression is therefore equal to

(x+1)(x+2)3(x+2)(x−2)(x+1)(x−1)=3(x−2)(x−1).

Note: One can of course expand the expression to get 3x2−9x+6 as the answer.