Calculus question, please help?

Question

Given the function f(x)=x^2, with a and x in the domain, a doesn’t equal x, then f(x) – f(a)/x – a equals:

a) x + a
b) 2x + 2a
c) x^2 + a^2
d) 2x

Answer 1

f(x) = x^2
f(a) = a^2

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

Answer 2

Supposing x different from 0, f(x) – f(a)/x – a = x^2 - a^2/x - a , none of the options given



But if you mean f(x) – f(a)/(x – a), x <>a, then it is (x^2 - a^2)/(x-a) = x+a.