Question

How do you simplify `(q^2+14q+48)/(q^2+q-30)`?

Answer 1

`(q+8)/(q-5)` for `q != -6` and `q != 5`

Explanation:

Notice that
`q^2+14q+48 = (q+6)(q+8)`
and
`q^2+q-30 = (q+6)(q-5)`

Therefore,
`(q^2+14q+48)/(q^2+q-30) = ((q+6)(q+8))/((q+6)(q-5))`

This expression is not defined for
`q = -6` and `q = 5`

For all other values of `q` we can reduce it by `q+6` to
`(q+8)/(q-5)`