Chapter P, Prerequisites - Section P.8 - Solving Basic Equations - P.8 Exercises - Page 60: 47

$x=\frac{13}{3}$

$\displaystyle \frac{3}{x+1}-\frac{1}{2}=\frac{1}{3x+3}$ We multiply both sides by $6(x+1)$: $3(6)-(3x+3)=2$ And distribute: $18-3x-3=2$ And simplify: $-3x+15=2$ And combine $x$ terms: $-3x=-13$ And solve for $x$: $x=\frac{13}{3}$