Question

Given f(x)= 2/x-1
Find f(5+h)-f(5)/h And simplify!

Answer 1

Please use parentheses
Given f(x)= 2/x-1
Find f(5+h)-f(5)/h And simplify
or do you mean
Given f(x)= 2 / (x-1)
Find { f(5+h)-f(5) } / h And simplify!

The second makes more sense if you are learning what the first derivative means

if the second
f(5+h) = 2 / (5+ h -1) = 2/(4+h)
f(5) = 2/4
{ f(5+h)-f(5) } = 2/(4+h) - 2/4 = [8 - 2(4+h) ] / [ 16+4h ]
= -2 h/ [16+4h] = -h/[ 8 + 2 h ]
divide by h
-1 / (2 h+8)
================================
now you are doing calculus so what happens if h-->0 ?
-1/8
check the derivative at x = 5
f(x) = 2/(x-1)
f'(x) = [-2*1] /(x-1)^2
if x = 5
f'(5) = -2 / 16 = -1/8 again the easy way