Answer
The equation has two solutions, $\frac{-3}{2}$ and $4$.
Work Step by Step
$\frac{3}{m-1}=\frac{2m}{m+4}$
$3(m+4)=2m(m-1)$ (Cross Products Property)
$3m+12=2m^2-2m$
$2m^2-5m-12=0$
$2m^2-8m+3m-12=0$
$2m(m-4)+3(m-4)=0$
$(2m+3)(m-4)=0$
$2m+3=0$ or $m-4=0$
$m=-\frac{3}{2}$ or $m=4$
Check:
$3/(4-1)=1; (2\times4)/(4+4)=1$
$3/(\frac{-3}{2}-1)=3\times\frac{-2}{5}=\frac{-6}{5}; (2\times\frac{-3}{2})/(\frac{-3}{2}+4)=(-3)\times\frac{2}{5}=-6/5$
The equation has two solutions, $\frac{-3}{2}$ and $4$.
