Difference quotient question: Given the function g(x) = x^2 + 2x, simplify g(x) − g(a)/x-a

Question

Hi, when I try to do this question, I get to the point of x^2 +2x-(a^2+2a)/x-a. I do not understand what to do from here. I'm guessing that there is some sort of way to factor out x-a in the numerator, so that you could cancel out x-a from both the numerator and the denominator. But I don't know how.

Answer 1

g(x) = x^2 +2x

g(a) = a^2 +2a

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

as x approaches a, the quotient approaches 2x+2 = g'(x)= the derivative of g(x)