Solution 2.1:8b

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m (Lösning 2.1:8b moved to Solution 2.1:8b: Robot: moved page)
Current revision (10:20, 25 September 2008) (edit) (undo)
 
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The fraction consists of the numerator
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<center> [[Image:2_1_8b.gif]] </center>
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<math>\frac{3}{x}-\frac{1}{x}</math>, which we can directly simplify somewhat to give
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<math>\frac{3}{x}-\frac{1}{x}=\frac{3-1}{x}=\frac{2}{x}</math>, and the denominator
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<math>\frac{1}{x-3}</math>. If we are to rewrite the fraction as an expression with a single fraction sign, we need
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to augment the multiply the top and bottom of the whole fraction by
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<math>x\left( x-3 \right)</math>
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and then eliminate
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<math>x</math>
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and
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<math>x-3</math>:
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<math>\begin{align}
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& \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)} \\
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& \\
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& =\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} \\
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\end{align}</math>

Current revision

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}

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