Chapter 11 - Rational Expressions and Functions - 11-5 Solving Rational Equations - Practice and Problem-Solving Exercises - Page 684: 37

$s=-1, -\frac{6}{5}$

Given:$\dfrac{s}{3s+2}+\dfrac{s+3}{2(s-2)}=\dfrac{-2s}{(3s+2)(s-2)}$ Need to find least common denominator(LCD). LCD: $2(3s+2)(s-2)$ $\dfrac{2s(s-2)}{2(3s+2)(s-2)}+\dfrac{(s+3)(3s+2)}{2(s-2)(3s+2)}=\dfrac{-2s .2 }{2(3s+2)(s-2)}$ $2s^2-4s+11s+6+3s^2+4s=0$ $5s^2+11s+6=0$ $5s^2+5s+6s+6=0$ $(s+1)(5s+6)=0$ Hence, $s=-1, -\frac{6}{5}$