Checkpoint: Restrictions for Rational Expressions Solutions

Determine the restrictions for the denominator.

$\frac{5 x - 8}{40 x^{3} + 11 x^{2} - 2 x}$

$\begin{array}{rcl} 40 x^{3} + 11 x^{2} - 2 x \\ x (40 x^{2} + 11 x - 2) \\ x (5 x + 2) (8 x - 1) \\ \begin{matrix} x = 0 & 5 x + 2 = 0 & 8 x - 1 = 0 \\ x = - \frac{2}{5} & x = \frac{1}{8} \end{matrix} \end{array}$

$x \neq - \frac{2}{5}, 0, \frac{1}{8}$

Note

Q: Why do you need to factor the denominator?
A: So the values that restrict the denominator can be found.

Q: Why is it not possible to have the value zero in the denominator?
A: Because you cannot divide something into zero groups.