((1/x+h)-(1/x))/h?

Question

This starts out as:
f(x)=1/x
I need to find and simplify using the difference quotient:
f(x+h) - f(x)
---------------
h

I have gotten as far as:
1/x+h - 1/x
--------------
h

The final answer is:
- 1
--------
x(x+h)

But I need to figure out the step(s) to that point.

Answer 1

puting x+h instead of x
f(x+h)=1/(x+h)
f(x+h)-f(x)
=1/(x+h)-1/x
cross multiply
=(x-x-h)/x(x+h)
=-h/x(x+h)
so
f(x+h)-f(x)=-h/(x(x+h))
f(x+h)-f(x)/h=-h/(x(x+h))/h
= -1/(x(x+h))





hope you will get it

Answer 2

[ 1 / (x + h) - 1 / x ] / h
[ (x - (x + h) / (x + h) (h) ] / h
(- h) / (x + h) (x) (h)
- 1 / (x + h) (x)

Answer 3

1/x+h - 1/x

=(x - (x+h))/((x+h)(x))
= (x - x-h)/((x+h)(x))
= - h/((x+h)(x))

so
1/x+h - 1/x
--------------
h

= - h/((x+h)(x))
--------------------
h
=
- 1
--------
x(x+h)

Answer 4

The answer to ((1/x+h)-(1/x))/h?
is 1

you basically have (n)/h where:

n = (1/x + h) - (1/x)
or (1/x) + h - (1/x)
or (1/x) - (1/x) + h
or ((1/x) - (1/x)) + h
or h

so h/h = 1

You looked into it too deep. Just look at the ()s

It is always in the details. Those of you who skim the details will find yourself wrong.

Answer 5

Given f(x) = 1/x:

[f(x + h) - f(x)] / [(x + h) - x] = [f(x + h) - f(x)] / h

= [1/(x + h) - 1/x] / h

= {x/[x(x + h)] - (x + h)/[x(x + h)]} / h

= {[x - (x + h)] / [x(x + h)]} / h

= {-h / [x(x + h)]} / h

= -1 / [x(x + h)]

Answer 6

f(x) = 1/x
f(x+h) = 1/(x+h)

f(x+h) - f(x) = 1/(x+h) - 1/x
= [x - (x+h)] / [x(x+h)]
= -h/(x(x+h))

[f(x+h) - f(x)]/h = -1/(x(x+h))