I have f (x) = x^2+x+5. Then (f (x) - f (a)) / (x-a).

(f (x) - f (a)) / (x - a) = x + a + 1

Step-by-step explanation:

(f (x) - f (a)) / (x - a) = ((x^2 + x + 5) - (a^2 + a + 5)) / (x - a) = (x^2 - a^2 + x - a) / (x - a)

= ((x - a) (x + a) + (x - a)) / (x - a) = x + a + 1

(f (x) - f (a)) / (x - a) = x + a + 1