Lösung 2.1:5c

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The fraction can be further simplified if it is possible to factorize and eliminate common factors
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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
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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:
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{{Displayed math||<math>\begin{align}
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<math>\begin{align}
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3x^{2}-12 &= 3(x^{2}-4) = 3(x+2)(x-2)\,,\\
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& 3x^{2}-12=3\left( x^{2}-4 \right)=3\left( x+2 \right)\left( x-2 \right) \\
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x^{2}-1 &= (x+1)(x-1) \,\textrm{.}
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& \\
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\end{align}</math>}}
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& x^{2}-1=\left( x+1 \right)\left( x-1 \right) \\
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\end{align}</math>
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The whole expression is therefore equal to
The whole expression is therefore equal to
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{{Displayed math||<math>\frac{3(x+2)(x-2)(x+1)(x-1)}{(x+1)(x+2)} = 3(x-2)(x-1)\,\textrm{.}</math>}}
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<math>\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)</math>
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Note: One can of course expand the expression to get <math>3x^{2}-9x+6</math>
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NOTE: One can of course expand out the expression to get
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<math>3x^{2}-9x+6</math>
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as the answer.
as the answer.

Version vom 10:57, 23. Sep. 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

Vorlage:Displayed math

The whole expression is therefore equal to

Vorlage:Displayed math

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

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_2.1:5c“