Final answer:
The excluded value of x in the rational expression f(x) = (x² + 7x)/(x² + 14x + 49) - 7 is x = -7.
Step-by-step explanation:
When determining the excluded values of a rational expression, we need to find the values of x that would result in a denominator equal to zero. In this case, the expression is f(x) = (x² + 7x)/(x² + 14x + 49) - 7. So, we set the denominator, x² + 14x + 49, equal to zero and solve for x.
x² + 14x + 49 = 0
This equation can be rewritten as (x + 7)(x + 7) = 0, which means x = -7 is the excluded value. Therefore, the excluded value of x in the rational expression f(x) is x = -7.