Find the value of [𝑓(𝑥)−𝑓(3)]/x-3 for each of the following functions

Question

Find the value of [𝑓(𝑥)−𝑓(3)]/x-3 for each of the following functions

𝑓(𝑥)=3𝑥^2 −2𝑥+1

𝑓(𝑥)=6/x

please do two of them, show all works

Answer 1

f(x) - f(3) = 3x^2-2x+1 - [ 3*3^2 - 2*3+1]

= 3x^2-2x+1 - [3*9-2*3+1]

= 3x^2-2x+1 - [27-6+1]

= 3x^2-2x+1 - [21+1]

= 3x^2 -2x +1 - 22

= 3x^2 -2x - 21

= (3x + 7)(x - 3)

the quotient is 3x+7

f(x)-f(3) = 6/x - 6/3 = 6/x - 2

= 6/x - (2x)/x

= (6-2x)/x

= 2(3-x)/x

= -2(x-3)/x

the quotient is -2/x