Given:
The expression is:
[tex]\dfrac{g^2+7g+12}{g^2-2g-24}[/tex]
To find:
The domain restrictions of the given expression.
Solution:
We have,
[tex]\dfrac{g^2+7g+12}{g^2-2g-24}[/tex]
To find the domain restrictions, we need to find the input values such that the denominator is equal to 0.
[tex]g^2-2g-24=0[/tex]
Splitting the middle term, we get
[tex]g^2-6g+4g-24=0[/tex]
[tex]g(g-6)+4(g-6)=0[/tex]
[tex](g-6)(g+4)=0[/tex]
Using zero product property, we get
[tex](g-6)=0[/tex] and [tex](g+4)=0[/tex]
[tex]g=6[/tex] and [tex]g=-4[/tex]
Therefore, the domain restrictions of the expression are -4 and 6. It means domain is set of all real numbers except -4 and 6.
