Final answer:
To evaluate g(-4+h)-g(-4)/h, substitute the values into the given function and simplify the expression to -7/h(h+1).
Step-by-step explanation:
To evaluate g(-4+h)-g(-4)/h, we need to substitute the given values into the function g(x) and simplify the expression.
Start by substituting -4+h into the function g(x):
g(-4+h) = 7/(-4+h+5) = 7/(h+1)
Next, substitute -4 into the function g(x):
g(-4) = 7/(-4+5) = 7/1 = 7
Now, substitute these values back into the expression:
(7/(h+1)) - 7/h
Common denominator is h(h+1), so multiply the first term by h and the second term by h+1:
(7h - 7(h+1))/h(h+1) = (7h - 7h - 7)/h(h+1) = -7/h(h+1)
Therefore, g(-4+h)-g(-4)/h simplifies to -7/h(h+1).