Lösung 2.1:8b
Aus Online Mathematik Brückenkurs 1
K (hat „Solution 2.1:8b“ nach „Lösung 2.1:8b“ verschoben: Robot: moved page) |
Version vom 13:52, 22. Okt. 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}
