Question

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?

Answer 1

We have that `(h(t))/g(t)=(2-t)/(3t+15)` and the domain of `(h(t))/g(t)` is `R-{0,-5}`

Explanation:

We have that

`(h(t))/g(t)=((2-t)/t)/((3t+15)/t)=(2-t)/(3t+15)`

The domain of `(h(t))/g(t)` is `R-{0,-5}`

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.