Given f(x)= 1/x. Simplify f(x+h) and (f(x+h)-f(x))/ h?

Question

I'm trying to review and i have no idea how to answer this problem.

Answer 1

Well, f(x+h) means replace the x in f(x) with (x+h) so

f(x+h) would be 1/(x+h)

Now you need to see what 1/(x+h) - 1/x is then put it over h.  To do that you need to get the common denominator which is x(x+h).  So the first expression is now x/[x(x+h)] and the second is (x+h)/[x(x+h)].

When you do the subtraction you get -h / [x(x+h)] and this is over h

So the h's cancel leaving -1 / [x(x+h)]