Im stuck on a college algebra problem. Help please?

Question

Evaluate the fuctions at the given values of the idenpendant variables. Simplify the results.

f(x) = 1 / Sqrrt(x-1)


f(x) - f(2)
-----------
x - 2

Please give a detailed explanation.
Thanks :)

Your all wrong so far.. anyone else?

Answer 1

f(x) is given;

f(2) means substitute 2 for x in the formula, or
f(2) = 1/sqrt(x-1) becomes
= 1/sqrt(2-1) or
= 1/sqrt(1)
= 1.

SO, f(x) - f(2) 1/sqrt(x-1) - 1
-------------- = ----------------------
x - 2 x - 2

1/sqrt(x-1) - sqrt(x-1)/sqrt(x-1)
= ---------------------------------------------
x - 2
1 - sqrt(x-1)
= ------------------------------
(x-2) sqrt(x-1)

rationalize denominator
(1 - sqrt(x-1))* sqrt(x-1)
= -------------------------------------
(x-2) (x-1)

sqrt(x-1) - (x-1)
= ----------------------
(x-2)(x-1)

Answer 2

First evaluate f(x) - f(2):
= 1/√(x-1) - 1/√(2-1)
= 1/√(x-1) - 1
= √(x-1)/(x-1) - (x-1)/(x-1)
= (√(x-1)-x+1)/(x-1)

(f(x) - f(2))/(x-2)
= (√(x-1)-x+1)/(x-1)(x-2)

That's as far as i can go.