Evaluate the difference quotient for the given function. Simplify your answer.
Answer 1
First find f(4):
f(4) = (4 + 8) / (4 + 2) = 12/6 = 2
So:
[f(x) – f(4)] / (x-4)
Insert f(x):
= [((x + 8)/(x+2)) – 2] / (x-4)
Multiply everything by (x+2):
= [(x + 8) – 2(x + 2)] / [(x – 4)(x +2)]
= (x + 8 – 2x – 4) / (x² – 2x – 8)
= (4 – x) / [(x – 4)(x + 2)]
= -(x – 4) / [(x – 4)(x+2)]
= -1 / (x + 2)