Answer:
The correct answer is option B.
Step-by-step explanation:
The given rational expression is:
[tex]\frac{x^2-4}{x^2+5x+6}[/tex]
Factor the numerator and the denominator:
[tex]\frac{x^2-2^2}{x^2+2x+3x+6}[/tex]
Factor the numerator using difference of two squares and the denominator using factorization by grouping.
[tex]\frac{(x-2)}{x(x+2)+3(x+2)}[/tex]
[tex]\frac{(x-2)(x+2)}{(x+2)(x+3)}[/tex]
This function is defined if and only if the denominator is not zero.
That is: (x+3)(x+2)≠0.
x≠-2,x≠-3
We simplify now to obtain:
[tex]\frac{x-2}{x+3}[/tex]
The correct choice is the second option.
