Answer
$\dfrac{z - 3}{2(z + 3)}$
The only restriction we have for $z$ is that $z \ne -3$.
Work Step by Step
To solve these types of problems, we want to remove greatest common factors in both the numerator and denominator. Hopefully, we will find that
For this problem, in the numerator, we can factor out a $4$, whereas in the denominator, we can factor out an $8$:
$\dfrac{4(z - 3)}{8(z + 3)}$
We can divide both numerator by $4$ to simplify the fraction:
$\dfrac{z - 3}{2(z + 3)}$
To see what restrictions for the variable we have, we need to see which values for the variable will make the denominator equal to $0$, which will cause the fraction to become undefined. Let's set the denominator equal to $0$ to see which values for the variable we cannot use:
$8z + 24 = 0$
Subtract $24$ from both sides of the equation to isolate the $z$ term:
$8z = -24$
Divide both sides of the equation by $8$ to solve for $z$:
$z = -3$
The only restriction we have for $z$ is that $z \ne -3$.
