Answer
$\left\{-\dfrac{5}{3},-\dfrac{3}{2}\right\}$
Work Step by Step
Multiplying both sides by the $LCD=
s^2
,$ the given equation, $
6+\dfrac{15}{s^2}=-\dfrac{19}{s}
,$ is equivalent to
\begin{align*}
s^2\left(6+\dfrac{15}{s^2}\right)&=\left(-\dfrac{19}{s}\right)s^2
\\\\
s^2(6)+1(15)&=-19(s)
\\
6s^2+15&=-19s
\\
6s^2+19s+15&=0
.\end{align*}
Using factoring of trinomials, the equation above is equivalent to
\begin{align*}
(3s+5)(2s+3)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property) and solving the variable, then
\begin{array}{l|r}
3s+5=0 & 2s+3=0
\\
3s=-5 & 2s=-3
\\
s=-\dfrac{5}{3} & s=-\dfrac{3}{2}
.\end{array}
Hence, the solution set of the equation $
6+\dfrac{15}{s^2}=-\dfrac{19}{s}
$ is $\left\{-\dfrac{5}{3},-\dfrac{3}{2}\right\}$.
