http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?action=history&feed=atom&title=Solution_2.1%3A7a 2026-04-08T11:48:32Z Revision history for this page on the wiki MediaWiki 1.11.1 http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.1:7a&diff=5431&oldid=prev 2008-09-23T11:55:10Z

<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 11:55, 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>If we multiply the top and bottom of the first fraction by</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>If we multiply the top and bottom of the first fraction by &lt;math&gt;x+5&lt;/math&gt; and the second by &lt;math&gt;x+3&lt;/math&gt;, then they will both have the same <ins style="color: red; font-weight: bold; text-decoration: none;">denominator </ins>and we can work out the expression by subtracting the numerators</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;x+5&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>and the second by</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+3&lt;/math&gt;, then they will both have the same <del style="color: red; font-weight: bold; text-decoration: none;">numerator </del>and we can work out the expression by subtracting the numerators<del style="color: red; font-weight: bold; text-decoration: none;">:</del></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;\begin{align}</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;\begin{align}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\frac{2}{x+3}-\frac{2}{x+5} <ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= \frac{2}{x+3}\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>\frac{x+5}{x+5}-\frac{2}{x+5}\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>\frac{x+3}{x+3}\\<ins style="color: red; font-weight: bold; text-decoration: none;">[7pt] </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;">&amp; </del>\frac{2}{x+3}-\frac{2}{x+5}=\frac{2}{x+3}\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\frac{x+5}{x+5}-\frac{2}{x+5}\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\frac{x+3}{x+3} \\ </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&amp;= \frac{2(x+5)-2(x+3)}{(x+3)(x+5)}<ins style="color: red; font-weight: bold; text-decoration: none;">\\[5pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&amp; =\frac{2<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( x+5 <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)-2<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( x+3 <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+3 <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+5 <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)}=\frac{2x+10-2x-6}{<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( x+3 <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+5 <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)}=\frac{4}{<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( x+3 <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+5 <del style="color: red; font-weight: bold; text-decoration: none;">\right</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;">&amp;</ins>= \frac{2x+10-2x-6}{(x+3)(x+5)}<ins style="color: red; font-weight: bold; text-decoration: none;">\\[5pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\end{align}&lt;/math&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;">&amp;</ins>= \frac{4}{(x+3)(x+5)}\<ins style="color: red; font-weight: bold; text-decoration: none;">,</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">textrm{.} </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>\end{align}&lt;/math&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">}}</ins></div></td></tr> </table>

Tek http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_2.1:7a&diff=5219&oldid=prev 2008-09-16T12:38:00Z

<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 12:38, 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;">If we multiply the top and bottom of the first fraction by</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_7a.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>&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+5</ins>&lt;/<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>&gt;</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><ins style="color: red; font-weight: bold; text-decoration: none;">and the second 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><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;x+3&lt;/math&gt;, then they will both have the same numerator and we can work out the expression by subtracting the numerators:</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;\begin</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">align}</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;">&amp; \frac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">2</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">{x+3</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">-\frac{2}{x+5}=\frac{2}{x+3}\centerdot \frac{x+5}{x+5}-\frac{2}{x+5}\centerdot \frac{x+3}{x+3} \\ </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;">&amp; =\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)} \\ </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;">\end{align}&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_2.1:7a&amp;action=edit" class="new" title="Lösning 2.1:7a">Lösning 2.1:7a</a> moved to <a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php/Solution_2.1:7a" title="Solution 2.1:7a">Solution 2.1:7a</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 08:40, 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_7a.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_7a.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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