# How do you find all the values that make the expression undefined: (3z^2 + z)/(18z + 6)?

Mar 23, 2018

$z = \text{no value}$

#### Explanation:

If you were to take the function as it is, then $18 z + 6 \ne 0$
$18 z \ne - 6$
$z \ne - \frac{6}{18} = - \frac{1}{3}$

However, we can simplify the function:
$\frac{z \left(3 z + 1\right)}{6 \left(3 z + 1\right)}$

$\frac{z \cancel{\left(3 z + 1\right)}}{6 \cancel{\left(3 z + 1\right)}} = \frac{z}{6}$ and therefore all values will be defined.