Lösung 2.1:7a

Aus Online Mathematik Brückenkurs 1

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If we multiply the top and bottom of the first fraction by
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If we multiply the top and bottom of the first fraction by <math>x+5</math> and the second by <math>x+3</math>, then they will both have the same denominator and we can work out the expression by subtracting the numerators
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<math>x+5</math>
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and the second by
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<math>x+3</math>, then they will both have the same numerator and we can work out the expression by subtracting the numerators:
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{{Displayed math||<math>\begin{align}
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<math>\begin{align}
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\frac{2}{x+3}-\frac{2}{x+5} &= \frac{2}{x+3}\cdot \frac{x+5}{x+5}-\frac{2}{x+5}\cdot \frac{x+3}{x+3}\\[7pt]
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& \frac{2}{x+3}-\frac{2}{x+5}=\frac{2}{x+3}\centerdot \frac{x+5}{x+5}-\frac{2}{x+5}\centerdot \frac{x+3}{x+3} \\
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&= \frac{2(x+5)-2(x+3)}{(x+3)(x+5)}\\[5pt]
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& =\frac{2\left( x+5 \right)-2\left( x+3 \right)}{\left( x+3 \right)\left( x+5 \right)}=\frac{2x+10-2x-6}{\left( x+3 \right)\left( x+5 \right)}=\frac{4}{\left( x+3 \right)\left( x+5 \right)} \\
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&= \frac{2x+10-2x-6}{(x+3)(x+5)}\\[5pt]
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\end{align}</math>
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&= \frac{4}{(x+3)(x+5)}\,\textrm{.}
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\end{align}</math>}}

Version vom 11:55, 23. Sep. 2008

If we multiply the top and bottom of the first fraction by \displaystyle x+5 and the second by \displaystyle x+3, then they will both have the same denominator and we can work out the expression by subtracting the numerators

Vorlage:Displayed math

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_2.1:7a“