Use Two Different Methods to Simplify the Fraction $$\frac{z-\frac{z+4}{24}}{\frac{5}{6}+\frac{7}{4 z}}$$

Essay

Use two different methods to simplify the fraction. Explain each step of your work.
$$\frac{z-\frac{z+4}{24}}{\frac{5}{6}+\frac{7}{4 z}}$$