Hallo!
Wir bringen den gleichen nenner (12):
[tex] \\ \frac{1}{v} + \frac{1}{2v} + \frac{1}{3v} + \frac{1}{4v} = \frac{2}{v} - \frac{1}{1} \Leftrightarrow \\ \\ \frac{12}{12v} + \frac{6}{12v} + \frac{4}{12v} + \frac{3}{12v} = \frac{24}{12v} - \frac{12v}{12v} \Leftrightarrow \\ \\ \frac{25}{12v} = \frac{24-12v}{12v} \\ \\ 25=24-12v \\ \\ 12v=24-25 \\ \\ 12v=-1 \\ v= -\frac{1}{12} \\ [/tex]
Prüfen:
[tex] \frac{1}{- \frac{1}{12} } + \frac{1}{- \frac{2}{12} } + \frac{1}{- \frac{3}{12} } + \frac{1}{- \frac{4}{12} } = \frac{2}{- \frac{1}{12} } -1 \Leftrightarrow \\ \\ -12-6-4-3=-24-1 \\ -25=-25\ Wirklich[/tex]
