Answer
$z=\frac{18 \pm \sqrt{285}}{3}$.
Work Step by Step
S9)
$$
\begin{aligned}
\frac{21}{z-5}-\frac{13}{z^2-5 z} & =3 \\
\frac{21}{z-5}-\frac{13}{z(z-5)} & =3 \\
\frac{21 z-13}{z(z-5)} & =3 \\
21 z-13 & =3 z(z-5) \\
21 z-13 & =3 z^2-15 z \\
3 z^2-36 z+13 & =0
\end{aligned}
$$
The quadratic formula gives:
$$
\begin{aligned}
z & =\frac{-(-36) \pm \sqrt{(-36)^2-4(3)(13)}}{2(3)} \\
& =\frac{36 \pm \sqrt{1140}}{6} \\
& =\frac{36 \pm \sqrt{4 \cdot 285}}{6} \\
& =\frac{36 \pm 2 \sqrt{285}}{6} \\
& =\frac{18 \pm \sqrt{285}}{3} .
\end{aligned}
$$
