Final answer:
To simplify the rational expression (x^2-42)/(x^2+11x+3), factor the numerator and denominator. The simplified expression is (x-√42)(x+√42)/(x^2+11x+3). Exclude any values for x that make the denominator equal to zero.
Step-by-step explanation:
To simplify the rational expression (x^2-42)/(x^2+11x+3), we first factor the numerator and denominator.
The numerator (x^2-42) can be factored as the difference of squares: (x-√42)(x+√42).
The denominator (x^2+11x+3) cannot be factored further.
Therefore, the simplified rational expression is (x-√42)(x+√42)/(x^2+11x+3).
The numbers that must be excluded from the domain of the simplified rational expression are any values for x that make the denominator equal to zero. So, we set x^2+11x+3=0 and solve for x to find these values.