Lösung 2.1:5c
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:
\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.