Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
No jsMath TeX fonts found -- using image fonts instead.
These may be slow and might not print well.
Use the jsMath control panel to get additional information.
jsMath Control PanelHide this Message

jsMath

Solution 2.1:5c

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
Current revision (10:57, 23 September 2008) (edit) (undo)
m
 
Line 1: Line 1:
-
The fraction can be further simplified if it is possible to factorize and eliminate common factors
+
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
-
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:
+
-
 
+
{{Displayed math||<math>\begin{align}
-
<math>\begin{align}
+
3x^{2}-12 &= 3(x^{2}-4) = 3(x+2)(x-2)\,,\\
-
& 3x^{2}-12=3\left( x^{2}-4 \right)=3\left( x+2 \right)\left( x-2 \right) \\
+
x^{2}-1 &= (x+1)(x-1) \,\textrm{.}
-
& \\
+
\end{align}</math>}}
-
& x^{2}-1=\left( x+1 \right)\left( x-1 \right) \\
+
-
\end{align}</math>
+
The whole expression is therefore equal to
The whole expression is therefore equal to
 +
{{Displayed math||<math>\frac{3(x+2)(x-2)(x+1)(x-1)}{(x+1)(x+2)} = 3(x-2)(x-1)\,\textrm{.}</math>}}
-
<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>
+
Note: One can of course expand the expression to get <math>3x^{2}-9x+6</math>
-
 
+
-
 
+
-
NOTE: One can of course expand out the expression to get
+
-
<math>3x^{2}-9x+6</math>
+
as the answer.
as the answer.

Current revision

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.

Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_2.1:5c"