Question

$\frac{1}{v} + \frac{1}{2v} + \frac{1}{3v} + \frac{1}{4v} = \frac{2}{v} - 1$

v = ?

Rezolvare si proba

( Rezultatul de la sfarsitul cartii este $v = - \frac{1}{12}$ )

Answer 1

numitorul comun este 12 

12/12v+6/12v+4/12v+3/12v=2*12/12v-1   lasam asa si le scriem sub aceeasi linie de fractie

(12+6+4+3)/12v=24/12v-1
25/12v=24/12v-1   amplificam -1 cu 12v ca sa scapam de fractii
25=24-12v
24-12v=25
-12v=25-24
-12v=1
v= - 1/12

Answer 2

Hallo!

Wir bringen den gleichen nenner (12):
$\\ \frac{1}{v} + \frac{1}{2v} + \frac{1}{3v} + \frac{1}{4v} = \frac{2}{v} - \frac{1}{1} \Leftrightarrow \\ \\ \frac{12}{12v} + \frac{6}{12v} + \frac{4}{12v} + \frac{3}{12v} = \frac{24}{12v} - \frac{12v}{12v} \Leftrightarrow \\ \\ \frac{25}{12v} = \frac{24-12v}{12v} \\ \\ 25=24-12v \\ \\ 12v=24-25 \\ \\ 12v=-1 \\ v= -\frac{1}{12}$

Prüfen:

$\frac{1}{- \frac{1}{12} } + \frac{1}{- \frac{2}{12} } + \frac{1}{- \frac{3}{12} } + \frac{1}{- \frac{4}{12} } = \frac{2}{- \frac{1}{12} } -1 \Leftrightarrow \\ \\ -12-6-4-3=-24-1 \\ -25=-25\ Wirklich$