Final answer:
To find (f-g)(x), subtract g(x) from f(x). Simplify the expression by combining like terms. The domain of (f-g)(x) is the set of x-values for which the expression is defined.
Step-by-step explanation:
To find (f-g)(x), we need to subtract g(x) from f(x). So, (f-g)(x) = f(x) - g(x). Substituting the given functions, we have:
(f-g)(x) = [(2x-9)/(x+1)] - [(x²-4x-49)/(x²+6x+5)]
To simplify this expression, we need to have the same denominator for both fractions. Factoring the denominators, we get:
(f-g)(x) = [(2x-9)/(x+1)] - [(x²-4x-49)/[(x+1)(x+5)]]
Now, we can combine like terms and simplify further if needed. The domain of (f-g)(x) would be the set of all x-values for which the expression is defined, excluding any values that would result in a zero denominator.