Lösung 2.1:5c
Aus Online Mathematik Brückenkurs 1
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Version vom 13:48, 22. Okt. 2008
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(x^{2}-4) = 3(x+2)(x-2)\,,\\ x^{2}-1 &= (x+1)(x-1) \,\textrm{.} \end{align} |
The whole expression is therefore equal to
| \displaystyle \frac{3(x+2)(x-2)(x+1)(x-1)}{(x+1)(x+2)} = 3(x-2)(x-1)\,\textrm{.} |
Note: One can of course expand the expression to get \displaystyle 3x^{2}-9x+6 as the answer.
