Question

24 / 5z + 4 = 4/z-1

Answer 1

again, you have not used brackets were necessary,
is this what you mean (24/5z)+4=(4/z)-1 or (24/5z)+4=(4/z-1)

Answer 2

is this
\[ \frac{24}{5z+4 }=\frac{4}{z-1} \]

Answer 3

multiply by z-1 on both sides
mutliply by 5z+4 on both sides
then simplify where necessary