(f(x)-f(2))/(x-2)?

Question:f(x)=(x+4)/(x+2)

Answers:
f(x) = (x+4) / (x+2)
f(2) = (2+4) / (2+2) = 6/4 = 3/2, So...

[f(x) - f(2)] / (x-2)
= { [ (x+4) / (x+2) ] - 3/2 } / (x - 2)
= { [ 2(x+4) - 3(x+2) ] / [2(x+2)] } * [ 1 / (x - 2)]
= [ 2(x+4) - 3(x+2) ] / [2(x+2)(x-2)]
= (2x + 8 - 3x - 6) / [2(x+2)(x-2)]
= (-x + 2) / [2(x+2)(x-2)]
= - (x - 2) / [2(x+2)(x-2)]

The (x - 2) in the numerator cancels out with the (x - 2) in the denominator, so you get:

= -1 / [2(x+2)]
= -1 / (2x + 4)

Therefore, [f(x) - f(2)] / (x-2) = -1 / (2x + 4)

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