[tex]A)z=-1,-6[/tex]
1) Let's solve that equation, by taking the LCM (z,1) = z and then dividing by each former denominator and multiplying by its corresponding numerator.
[tex]\begin{gathered} z+\frac{6}{z}=-7 \\ \frac{\placeholder{⬚}}{z}+\frac{\placeholder{⬚}}{z}=\frac{\placeholder{⬚}}{z} \\ \frac{z^2}{z}+\frac{6}{z}=\frac{-7z}{z} \end{gathered}[/tex]
2) Now, we can multiply both sides by z to get rid of those denominators:
[tex]\begin{gathered} z\times\frac{z^{2}}{z}+\frac{6}{z}=\frac{-7z}{z}\times z \\ z^2+6=-7z \\ z^2+7z+6=0 \\ z_=\frac{-7\pm\sqrt{7^2-4\cdot\:1\cdot\:6}}{2\cdot\:1} \\ z=-1,z=-6 \end{gathered}[/tex]
CaAnd solve the quadratic equation with the formula.
