Simplify the difference quotient

Question

(f(x + h) - f(x))/h if h is not = to 0 Simplify the difference quotient. F(x)=X^2 t 21

Answer 1

f(x+h) = (x+h)^2 + 21 = x^2 +2xh + h^2 + 21

f(x+h) - f(x) = x^2 +2xh + h^2 + 21 - x^2 - 21 = 2xh + h^2

divide by h to get 2x + h

Answer 2

f(x+h) = (x+h)^2 + 21 = x^2 +2xh + h^2 + 21

f(x+h) - f(x) = x^2 +2xh + h^2 + 21 - x^2 - 21 = 2xh + h^2

divide by h to get 2x + h