From Förberedande kurs i matematik 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:

\displaystyle \begin{align} & 3x^{2}-12=3\left( x^{2}-4 \right)=3\left( x+2 \right)\left( x-2 \right) \\ & \\ & x^{2}-1=\left( x+1 \right)\left( x-1 \right) \\ \end{align}

The whole expression is therefore equal to

\displaystyle \frac{3\left( x+2 \right)\left( x-2 \right)\left( x+1 \right)\left( x-1 \right)}{\left( x+1 \right)\left( x+2 \right)}=3\left( x-2 \right)\left( x-1 \right)

NOTE: One can of course expand out the expression to get \displaystyle 3x^{2}-9x+6 as the answer.