# Let h(t) = (2-t)/(t) and g(t)= (3t+15)/t, how do you find (h/g)(t) and the domain for h/g?

##### 1 Answer

We have that $\frac{h \left(t\right)}{g} \left(t\right) = \frac{2 - t}{3 t + 15}$ and the domain of $\frac{h \left(t\right)}{g} \left(t\right)$ is $R - \left\{0 , - 5\right\}$

#### Explanation:

We have that

$\frac{h \left(t\right)}{g} \left(t\right) = \frac{\frac{2 - t}{t}}{\frac{3 t + 15}{t}} = \frac{2 - t}{3 t + 15}$

The domain of $\frac{h \left(t\right)}{g} \left(t\right)$ is $R - \left\{0 , - 5\right\}$

The domain of a quotient is a subset of the intersection of the domains. Since neither domain contains 0, the domain of the quotient excludes 0 as well.