Answer
The solution is $v=-2$ or $v=-6$.
Work Step by Step
$\frac{v}{3}+\frac{v}{v+5}=\frac{-4}{v+5}$
Add:
$\frac{v(v+5)}{3(v+5)}+\frac{3v}{3(v+5)}=\frac{-12}{3(v+5)}$
$v^2+5v+3v=-12$
Simplify:
$v^2+8v+12=0$
Factor:
$(v+2)(v+6)=0$
$v=-2$ or $v=-6$
Check:
$\frac{-2}{3}+\frac{-2}{-2+5}=\frac{-4}{-2+5}$
$\frac{-4}{3}=\frac{-4}{3}$
$\frac{-6}{3}+\frac{-6}{-6+5}=\frac{-4}{-6+5}$
$4=4$
The solution is $v=-2$ or $v=-6$.
