Question

if f(x) = (x-1)/x and (f(x+h)-f(x))/h ... what is the answer.. so lost

Answer 1

\[f(x)=\frac{ x-1 }{ x }\]

Answer 2

\[and \frac{ f(x+h)-f(x) }{ h }\]

Answer 3

lets go real real slow
it is a raft of algebra
the first thing you need to write is what
\[f(x+h)\] is
do you know it ?

Answer 4

no is a fine answer, i am just asking

Answer 5

i know that i need to place it exactly where x is in the problem but confused about where there is 2 functions

Answer 6

@satellite73 do i put the them in like this?\[\frac{ \frac{ f(x+h)-f(x)-h }{ h } }{ \frac{ f(x+h)-f(x) }{ } }\]

Answer 7

there's an h on the bottom that got cut off

Answer 8

leaving me with \[\frac{ f(x+h)-f(x)-h }{ f(x+h)-f(x) }\]

Answer 9

oh no no hold the phone for a second
you are doing too much and too little

Answer 10

i think i did it.. another way obviously.. should i get 1 as the final answer?

Answer 11

like i said lets go slow
first of all \(f\) is not some general \(f\) it is a specific \(f\)

Answer 12

no you do not get number for an answer

Answer 13

i see you are confused by this so lets go slow
\[f(x)=\frac{ x-1 }{ x }\]
\[f(x+h)=?\]

Answer 14

you have to replace \(x\) in \(\frac{x-1}{x}\) by \(x+h\)

Answer 15

making
\[f(x+h)=\frac{x+h-1}{x+y}\]

Answer 16

ok, understood

Answer 17

damn typo
\[f(x+h)=\frac{x+h-1}{x+h}\]

Answer 18

now we have
\[f(x+h)\] next we need
\[f(x+h)-f(x)\] this is where the algebra comes in

Answer 19

\[f(x+h)-f(x)=\frac{x+h-1}{x+h}-\frac{x-1}{x}\] before the algebra
your next job is to subtract

Answer 20

well we have a common denominator... correct?

Answer 21

pellet nvm

Answer 22

thats my stupid mistake

Answer 23

yes of course
leave everything in factored form

Answer 24

i wrote x as denominator when i shouldve had x+h

Answer 25

no careful here
\[\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}\] the common denonminator of \(x\) and \(x+h\) is NOT \(x+h\) just like the common denominator for \(5\) and \(5+2\) is not \(7\)

Answer 26

don't do any multiplying out
just write it
leave it in factored form

Answer 27

my final answer comes out to be \[\frac{ h }{ x(x+h) }\]

Answer 28

maybe let me check

Answer 29

yeah good work

Answer 30

so then the hs cancel and im left with 1/x+h

Answer 31

now divide by \(h\) i.e. cancel the \(h\)

Answer 32

what happened to the other \(x\) ?

Answer 33

sorry typo

Answer 34

\[\frac{ 1 }{ x(x+h) }\]

Answer 35

you win

Answer 36

thanks

Answer 37

yw