[tex]\dfrac{z-1}3 = \dfrac8{z+1}[/tex]
Eliminate the denominators.
[tex]3(z+1)\cdot\dfrac{z-1}3 = 3(z+1)\cdot\dfrac8{z+1}[/tex]
[tex]z^2 - 1 = 24[/tex]
Solve for [tex]z[/tex].
[tex]z^2 = 25[/tex]
[tex]\boxed{z = \pm5}[/tex]
