Question

What are the domain restrictions of the expression g2+7g+12/g2−2g−24 ?

Answer 1

Given:

The expression is:

`(g^2+7g+12)/(g^2-2g-24)`

To find:

The domain restrictions of the given expression.

Solution:

We have,

`(g^2+7g+12)/(g^2-2g-24)`

To find the domain restrictions, we need to find the input values such that the denominator is equal to 0.

`g^2-2g-24=0`

Splitting the middle term, we get

`g^2-6g+4g-24=0`

`g(g-6)+4(g-6)=0`

`(g-6)(g+4)=0`

Using zero product property, we get

`(g-6)=0` and
`(g+4)=0`

`g=6` and
`g=-4`

Therefore, the domain restrictions of the expression are -4 and 6. It means domain is set of all real numbers except -4 and 6.