Evaluate the difference quotient for the given function. Simplify your answer.

Question

f(x) = (x + 8) / (x + 3) , f(x) - f(2) / (x - 2)

Answer 1

f(2) = 2

f(x) - f(2) = [(x + 8) / (x + 3)] - 2

f(x) - f(2) = [(x + 8) - 2(x + 3)] / (x + 3)

f(x) - f(2) = [(-x + 2) / (x + 3)]

[f(x) - f(2)] / (x + 2) = [(-x + 2) / (x + 3)(x - 2)]

[f(x) - f(2)] / (x - 2) = [-(x - 2) / (x + 3)(x - 2)]

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

Answer 2

Given f(x) = (x + 8) / (x + 3) , fund f(x) - f(2) / (x - 2),

f(2) = ( 2+8) / ( 2+3) = 10/5 = 2

f(x) - f(2) / (x - 2) = (x + 8) / (x + 3) - 2 / ( x-2) = { [ ( x+ 8) - 2( x+3) ] / (x+3) } / (x-2) = [ x+8 - 2x -6] / ( x+3)(x-2)

= ( 2-x) / ( x+3)(x-2) = -( x-2) / ( x+3)(x-2) cancel ( x-2) from the numerator and the denominator

f(x) - f(2) / (x - 2),= -1/ ( x+3)