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What are the domain restrictions of the expression g2+7g+12/g2āˆ’2gāˆ’24 ?

Sagot :

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.

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