# How do you find the domain of f(x)=(2x)/((x-2)(x+3))?

Jul 18, 2017

The denominatos can't be zero.

#### Explanation:

The only contraint is : $\left(x - 2\right) \left(x + 3\right) \ne 0 \iff x \ne 2 \mathmr{and} x \ne - 3$

so the domain is then $D = x \in \mathbb{R} - \left\{- 3 , 2\right\}$

Jul 18, 2017

$x \in \mathbb{R} , x \ne - 3 , 2$

#### Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be.

$\text{solve } \left(x - 2\right) \left(x + 3\right) = 0$

$\Rightarrow x = - 3 \text{ and " x=2larrcolor(red)" are excluded values}$

$\text{domain is } x \in \mathbb{R} , x \ne - 3 , 2$