find f(a+h) - f(a)
___________
h for f(x) = 1
_____
x-3

Question

find f(a+h) - f(a)
        ___________
                h                             for f(x) = 1 
                                                             _____
                                                             x-3

anonymous · Answer

you are basically plugging in F(x) everywhere you see a.

anonymous · Answer

actually that is not quite correct

anonymous · Answer

$$f(a)=\frac{1}{a-3}$$
$$f(a+h)=\frac{1}{a+h-3}$$
$$f(a+h)-f(a)=\frac{1}{a+h-3}-\frac{1}{a-3}$$
$$=\frac{-h}{(a+h-3)(a-3)}$$

anonymous · Answer

never seen it done that way, but ok I trust you. Thanks

anonymous · Answer

then divide by h and get 
$$\frac{-1}{(a+h-3)(a-3)}$$

anonymous · Answer

the weird thing is none of my possible answers have a -1..but all have 1s

anonymous · Answer

hold on let me check my algebra

anonymous · Answer

okay

anonymous · Answer

answer i wrote it correct. you are probably getting ready to take the derivative, which would be doing the same algebra and then letting h go to zero, and you should get 
$$-\frac{1}{(a-3)^2}$$so i know it is correct. 
perhaps your possible answer is 
$$-\frac{1}{(a+h-3)(a-3)}$$ with the minus sign out front instead of next to the 1 in the numerator
it is the same thing

anonymous · Answer

THANK YOU SO MUCH!!!