Answer
The equation has one solution, 3.
Work Step by Step
$\frac{r+1}{r-1}=\frac{r}{3}+\frac{2}{r-1}$
$3(r-1)\frac{r+1}{r-1}=3(r-1)(\frac{r}{3}+\frac{2}{r-1})$
$3(r+1)=\frac{3(r-1)r}{3}+\frac{6(r-1)}{r-1}$
$3r+3=r(r-1)+6$
$3r+3=r^2-r+6$
$r^2-4r+3=0$
$(r-1)(r-3)=0$
$r-1=0$ or $r-3=0$
$r=1$ or $r=3$
Check:
$(1+1)/(1-1)=2/0$ (undefined)
$(3+1)/(3-1)=4/2=2; 3/3+2/(3-1)=1+1=2$
The equation has one solution, 3.
