http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?action=history&feed=atom&title=Solution_2.1%3A8a 2026-04-08T12:00:01Z Revision history for this page on the wiki MediaWiki 1.11.1 http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.1:8a&diff=5435&oldid=prev 2008-09-23T12:29:56Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 12:29, 23 September 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>An expression which consists of several fraction signs can be rewritten in terms of one fraction sign</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>An expression which consists of several fraction signs can be rewritten in terms of one fraction sign by systematically eliminating all partial fractions. </div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>by systematically eliminating all partial fractions. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In our expression, we multiply the top and bottom of the main fraction by </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In our expression, we multiply the top and bottom of the main fraction by &lt;math&gt;x+1&lt;/math&gt; (so as to get rid of &lt;math&gt;x+1&lt;/math&gt; from the numerator),</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;x+1&lt;/math&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>(so as to get rid of </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;x+1&lt;/math&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>from the numerator),</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">{{Displayed math||</ins>&lt;math&gt;\frac{\<ins style="color: red; font-weight: bold; text-decoration: none;">,\dfrac</ins>{x}{x+1}<ins style="color: red; font-weight: bold; text-decoration: none;">\,</ins>}{3+x} = \frac{\<ins style="color: red; font-weight: bold; text-decoration: none;">,\dfrac</ins>{x}{x+1}<ins style="color: red; font-weight: bold; text-decoration: none;">\,</ins>}{3+x}\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\frac{x+1}{x+1} = \frac{\<ins style="color: red; font-weight: bold; text-decoration: none;">,\dfrac</ins>{x}{x+1}\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>(x+1)<ins style="color: red; font-weight: bold; text-decoration: none;">\,</ins>}{\<ins style="color: red; font-weight: bold; text-decoration: none;">,</ins>(3+x)(x+1<ins style="color: red; font-weight: bold; text-decoration: none;">)</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">,</ins>} = \frac{x}{(3+x)(x+1)}<ins style="color: red; font-weight: bold; text-decoration: none;">\,\textrm{</ins>.<ins style="color: red; font-weight: bold; text-decoration: none;">}</ins>&lt;/math&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">}}</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;\frac{\<del style="color: red; font-weight: bold; text-decoration: none;">frac</del>{x}{x+1}}{3+x}=\frac{\<del style="color: red; font-weight: bold; text-decoration: none;">frac</del>{x}{x+1}}{3+x}\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\frac{x+1}{x+1}=\frac{\<del style="color: red; font-weight: bold; text-decoration: none;">frac</del>{x}{x+1}\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot \left</del>( x+1 <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)}{\<del style="color: red; font-weight: bold; text-decoration: none;">left</del>( 3+x <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( x+1 \<del style="color: red; font-weight: bold; text-decoration: none;">right)</del>}=\frac{x}{<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( 3+x <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( x+1 <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)}.&lt;/math&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> </table>

Tek http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.1:8a&diff=5222&oldid=prev 2008-09-16T13:08:07Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 13:08, 16 September 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">{{NAVCONTENT_START}}</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">An expression which consists of several fraction signs can be rewritten in terms of one fraction sign</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;<del style="color: red; font-weight: bold; text-decoration: none;">center</del>&gt; <del style="color: red; font-weight: bold; text-decoration: none;">[[Image:2_1_8a.gif]] </del>&lt;/<del style="color: red; font-weight: bold; text-decoration: none;">center</del>&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">by systematically eliminating all partial fractions. </ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del style="color: red; font-weight: bold; text-decoration: none;">NAVCONTENT_STOP</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">In our expression, we multiply the top and bottom of the main fraction by </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">x+1</ins>&lt;/<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>&gt;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">(so as to get rid of </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;x+1&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">from the numerator),</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;\frac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">\frac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">x</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">{x+1</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">}{3+x}=\frac{\frac{x}{x+1}}{3+x}\centerdot \frac{x+1}{x+1}=\frac{\frac{x}{x+1}\centerdot \left( x+1 \right)}{\left( 3+x \right)\left( x+1 \right)}=\frac{x}{\left( 3+x \right)\left( x+1 \right)}.&lt;/math&gt;</ins></div></td></tr> </table>

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<p><a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=L%C3%B6sning_2.1:8a&amp;action=edit" class="new" title="Lösning 2.1:8a">Lösning 2.1:8a</a> moved to <a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php/Solution_2.1:8a" title="Solution 2.1:8a">Solution 2.1:8a</a>: Robot: moved page</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 08:41, 9 September 2008</td> </tr> </table>

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<p>Robot: Automated text replacement (-[[Bild: +[[Image:)</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 06:37, 21 August 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_START}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_START}}</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;center&gt; [[<del style="color: red; font-weight: bold; text-decoration: none;">Bild</del>:2_1_8a.gif]] &lt;/center&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;center&gt; [[<ins style="color: red; font-weight: bold; text-decoration: none;">Image</ins>:2_1_8a.gif]] &lt;/center&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_STOP}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_STOP}}</div></td></tr> </table>

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