I usually would never do this but... any math lovers? HELP.?

Question

My precalc teacher said she "had to go" after school, my mom doesn't know, my friends all say they don't remember how they did the problem, since this is last weeks stuff (hah!). So I'm completely stuck and I've been sitting here staring at what I have on the problem for half an hour

There's a stupid limit problem f(x)= 2/(x-1) at x=3, and I ended up with

((-h+3)/(h+1))/h

I despise fractions on fractions. I know I need to get rid of the bottom-most denominator. how the hell do I get rid of it so I can substitute? Thanks anyone who answers

Thank you Philo! I feel like an airhead because it was all because of a simple subtraction error :)

Answer 1

How did you end up with the h's?

Here is how you go about this problem:

f(x) = 2/(x-1) if x=3, then,
f(3)= 2/(3-1)
f= 2/3(3-1) = 2/9-3 = 2/6 = 1/3
therefore f=1/3

Answer 2

I think you're finding lim (h→0) of the difference quotient [ f(x+h) - f(x) ] / h at x=3, so you need

lim(h→0) [ 2/(3+h - 1) - 2/(3-1) ] / h =
lim(h→0) [ 2/(h + 2) - 1 ] / h =
lim(h→0) [ 2/(h + 2) - (h+2)/(h+2) ] / h =
lim(h→0) [ ( 2 - h - 2)/(h+ 2) ] / h =
lim(h→0) [ -h / (h+2) ] / h =

and now you divide by multiplying by reciprocal, just like 5th grade:

lim(h→0) [ -1 / (h+2) ] = -1 / (0+2) = -1/2