The domain restrictions apply to rational expression are:
[tex]x\neq 3\\\\x\neq -3[/tex]
Solution:
Given rational expression is:
[tex]\frac{x^2 + 5x + 6}{x^2 - 9}[/tex]
We have to find the domain restrictions apply to rational expression
From given,
[tex]\frac{x^2 + 5x + 6}{x^2 - 9}[/tex]
Use the identity,
[tex]a^2 - b^2 = (a+b)(a-b)[/tex]
Therefore,
[tex]\frac{x^2 + 5x + 6}{(x+3)(x-3)}[/tex]
The rational expression is undefined when denominator is 0
From above, see the denominator (x + 3) and (x - 3)
When x = -3 and x = 3, the denominator becomes 0
Thus, domain restrictions are:
[tex]x\neq 3\\\\x\neq -3[/tex]
