# What is the domain of ( 6 + 3x^(3) -4x^(2) -17x ) / ( x^(3) -3x^(2) -10x )?

Oct 1, 2015

Domain: $\mathbb{R} - \left\{- 2 , 0 , 5\right\}$

#### Explanation:

The given expression is valid for all values of $x$ except those for which the denominator is equal to zero.

${x}^{3} = 3 {x}^{2} - 10 x \ne 0$

Factoring:
$\left(x\right) \left(x - 5\right) \left(x + 2\right) \ne 0$

Therefore
$x \ne 0$ and $x \ne 5$ and $x \ne - 2$