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1.5 Lösning 5a - Versionshistorik
2026-06-27T00:16:25Z
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Taifun den 10 mars 2011 kl. 13.32
2011-03-10T13:32:31Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 10 mars 2011 kl. 13.32</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
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<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} (3^x + 3^{x+1}) \,/\, 4\; & = \; 9  \qquad | \; \cdot 4  \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} (3^x + 3^{x+1}) \,/\, 4\; & = \; 9  \qquad <ins class="diffchange diffchange-inline">\; </ins>| \; \cdot 4  \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                   3^x + 3^{x+1} & = \; 36 <del class="diffchange diffchange-inline">                    </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                   3^x + 3^{x+1} & = \; 36 <ins class="diffchange diffchange-inline">                        </ins>\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                             3^x + 3^x \cdot 3^1 & = \; 36 <del class="diffchange diffchange-inline">                    </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                             3^x + 3^x \cdot 3^1 & = \; 36 <ins class="diffchange diffchange-inline">                        </ins>\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                 3^x \cdot (1+3) & = \; 36 <del class="diffchange diffchange-inline">                    </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                 3^x \cdot (1+3) & = \; 36 <ins class="diffchange diffchange-inline">                        </ins>\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                     4 \cdot 3^x & = \; 36  \qquad | \<del class="diffchange diffchange-inline">, </del>/ 4 <del class="diffchange diffchange-inline">    </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                     4 \cdot 3^x & = \; 36  \qquad | \<ins class="diffchange diffchange-inline">; </ins>/ 4 <ins class="diffchange diffchange-inline">      </ins>\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                             3^x & = \;  9 <del class="diffchange diffchange-inline">                    </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                             3^x & = \;  9 <ins class="diffchange diffchange-inline">                        </ins>\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                             3^x & = \;  3^2 <del class="diffchange diffchange-inline">                  </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                             3^x & = \;  3^2 <ins class="diffchange diffchange-inline">                      </ins>\\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                               x & = \;  2</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                               x & = \;  2</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>         \end{align} </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>         \end{align} </math></div></td></tr>
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Taifun
https://minidemo.mathonline.se/index.php?title=1.5_L%C3%B6sning_5a&diff=3081&oldid=prev
Taifun den 10 mars 2011 kl. 13.15
2011-03-10T13:15:16Z
<p></p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 10 mars 2011 kl. 13.15</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} <del class="diffchange diffchange-inline">y_3 & = {2\,</del>x^<del class="diffchange diffchange-inline">2 </del>+ <del class="diffchange diffchange-inline">6</del>\,<del class="diffchange diffchange-inline">x </del>\<del class="diffchange diffchange-inline">over </del>x^<del class="diffchange diffchange-inline">2 - 9</del>} = <del class="diffchange diffchange-inline">{2</del>\<del class="diffchange diffchange-inline">,x</del>\<del class="diffchange diffchange-inline">,(</del>x + 3<del class="diffchange diffchange-inline">) </del>\<del class="diffchange diffchange-inline">over (</del>x + 3)\<del class="diffchange diffchange-inline">,(x - </del>3<del class="diffchange diffchange-inline">)} </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} <ins class="diffchange diffchange-inline">(3^</ins>x <ins class="diffchange diffchange-inline">+ 3</ins>^<ins class="diffchange diffchange-inline">{x</ins>+<ins class="diffchange diffchange-inline">1}) </ins>\,<ins class="diffchange diffchange-inline">/</ins>\<ins class="diffchange diffchange-inline">, 4\; & = \; 9  \qquad | \; \cdot 4  \\</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">                                                                                                    </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">                                  3^</ins>x <ins class="diffchange diffchange-inline">+ 3</ins>^<ins class="diffchange diffchange-inline">{x+1</ins>} <ins class="diffchange diffchange-inline">& </ins>= \<ins class="diffchange diffchange-inline">; 36                      </ins>\<ins class="diffchange diffchange-inline">\</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">                y_4 </del>& = <del class="diffchange diffchange-inline">{</del>2\<del class="diffchange diffchange-inline">,x </del>\<del class="diffchange diffchange-inline">over </del>x <del class="diffchange diffchange-inline">- 3}</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">                            3^</ins>x + 3<ins class="diffchange diffchange-inline">^x </ins>\<ins class="diffchange diffchange-inline">cdot 3^1 & = \; 36                      \\</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">                                3^</ins>x <ins class="diffchange diffchange-inline">\cdot (1</ins>+3) <ins class="diffchange diffchange-inline">& = </ins>\<ins class="diffchange diffchange-inline">; 36                      \\</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">                                    4 \cdot </ins>3<ins class="diffchange diffchange-inline">^x & = \; 36  \qquad | \, / 4    </ins>\\</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">                                            3^x & = \;  9                      </ins>\\</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">                                            3^x </ins>& = <ins class="diffchange diffchange-inline">\;  3^</ins>2 <ins class="diffchange diffchange-inline">                  </ins>\\</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">                                              </ins>x <ins class="diffchange diffchange-inline">& = \;  2</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>         \end{align} </math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>         \end{align} </math></div></td></tr>
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Taifun
https://minidemo.mathonline.se/index.php?title=1.5_L%C3%B6sning_5a&diff=3080&oldid=prev
Taifun: Created page with "::<math>\begin{align} y_3 & = {2\,x^2 + 6\,x \over x^2 - 9} = {2\,x\,(x + 3) \over (x + 3)\,(x - 3)} \\ ..."
2011-03-10T13:01:55Z
<p>Created page with "::<math>\begin{align} y_3 & = {2\,x^2 + 6\,x \over x^2 - 9} = {2\,x\,(x + 3) \over (x + 3)\,(x - 3)} \\ ..."</p>
<p><b>Ny sida</b></p><div>::<math>\begin{align} y_3 & = {2\,x^2 + 6\,x \over x^2 - 9} = {2\,x\,(x + 3) \over (x + 3)\,(x - 3)} \\<br />
\\<br />
y_4 & = {2\,x \over x - 3}<br />
\end{align} </math></div>
Taifun