# How do you find the domain of n(t)=(6t+5)/(3t+8)?

Jun 7, 2018

$x \in \mathbb{R} , x \ne - \frac{8}{3}$

#### Explanation:

The only time $n \left(t\right)$ will be undefined is when our denominator is equal to zero, as we know that we cannot divide by zero.

Let's just set the denominator equal to zero. We have

$3 t + 8 = 0$

Subtracting $8$ from both sides, we get

$3 t = - 8$

Dividing both sides by $3$, we get

$t = - \frac{8}{3}$

This is the only value that $n \left(t\right)$ is undefined, thus or domain is

$x \in \mathbb{R} , x \ne - \frac{8}{3}$

Hope this helps!