Answer:
[tex]Dom\{f(x)\}=\mathbb{R}-\{-3,1\}[/tex]
Step-by-step explanation:
The correct rational expression is [tex]f(x) = \frac{x^{2}+6\cdot x^{2}+6}{x^{2}+2\cdot x-3}[/tex]. From Algebra we know that rational polynomical expressions are continuous except for those values of x such that denominator equals zero. First, we factorize the polynomial at denominator:
[tex]x^{2}+2\cdot x-3 = (x+3)\cdot (x-1)[/tex]
Which means that domain is represented by the set of all real number except -3 and 1.
[tex]Dom\{f(x)\}=\mathbb{R}-\{-3,1\}[/tex]
