Lösung 2.1:8b

Aus Online Mathematik Brückenkurs 1

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Lösning 2.1:8b moved to Solution 2.1:8b: Robot: moved page)
Zeile 1: Zeile 1:
-
{{NAVCONTENT_START}}
+
The fraction consists of the numerator
-
<center> [[Image:2_1_8b.gif]] </center>
+
<math>\frac{3}{x}-\frac{1}{x}</math>, which we can directly simplify somewhat to give
-
{{NAVCONTENT_STOP}}
+
<math>\frac{3}{x}-\frac{1}{x}=\frac{3-1}{x}=\frac{2}{x}</math>, and the denominator
 +
<math>\frac{1}{x-3}</math>. If we are to rewrite the fraction as an expression with a single fraction sign, we need
 +
to augment the multiply the top and bottom of the whole fraction by
 +
<math>x\left( x-3 \right)</math>
 +
and then eliminate
 +
<math>x</math>
 +
and
 +
<math>x-3</math>:
 +
 
 +
 
 +
<math>\begin{align}
 +
& \frac{\frac{3}{x}-\frac{1}{x}}{\frac{1}{x-3}}=\frac{\frac{2}{x}}{\frac{1}{x-3}}=\frac{\frac{2}{x}}{\frac{1}{x-3}}\centerdot \frac{x\left( x-3 \right)}{x\left( x-3 \right)} \\
 +
& \\
 +
& =\frac{\frac{2}{x}\centerdot x\left( x-3 \right)}{\frac{1}{x-3}\centerdot x\left( x-3 \right)}=\frac{2\left( x-3 \right)}{x} \\
 +
\end{align}</math>

Version vom 10:20, 25. Sep. 2008

The fraction consists of the numerator \displaystyle \frac{3}{x}-\frac{1}{x}, which we can directly simplify somewhat to give \displaystyle \frac{3}{x}-\frac{1}{x}=\frac{3-1}{x}=\frac{2}{x}, and the denominator \displaystyle \frac{1}{x-3}. If we are to rewrite the fraction as an expression with a single fraction sign, we need to augment the multiply the top and bottom of the whole fraction by \displaystyle x\left( x-3 \right) and then eliminate \displaystyle x and \displaystyle x-3:


\displaystyle \begin{align} & \frac{\frac{3}{x}-\frac{1}{x}}{\frac{1}{x-3}}=\frac{\frac{2}{x}}{\frac{1}{x-3}}=\frac{\frac{2}{x}}{\frac{1}{x-3}}\centerdot \frac{x\left( x-3 \right)}{x\left( x-3 \right)} \\ & \\ & =\frac{\frac{2}{x}\centerdot x\left( x-3 \right)}{\frac{1}{x-3}\centerdot x\left( x-3 \right)}=\frac{2\left( x-3 \right)}{x} \\ \end{align}

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_2.1:8b“