anonymous
  • anonymous
find the difference quotient of f(x)= (2x)/(x-1)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@Nnesha can you please help me
Nnesha
  • Nnesha
we need to use formula f(x+h)-f(x) over h right ?
anonymous
  • anonymous
instead of x im using a but yes

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More answers

anonymous
  • anonymous
f(a)= (2a)/(a-1)
Nnesha
  • Nnesha
ohh okay so first we have to find f(a+h) substitute a for a+h
anonymous
  • anonymous
and f(a+h)= (2a+2h)/(-a-h)
anonymous
  • anonymous
am i correct
Nnesha
  • Nnesha
the denominator would be a-1 = (a+h)-1 so it would be a+h-1 it's not a multiplication
anonymous
  • anonymous
oh alright
Nnesha
  • Nnesha
alright so now we can substitute f(a+h) for that into the formula \[\huge \rm \frac{ \frac{ 2a+2h }{ a+h-1 } +\frac{ 2a }{ a-1 } }{ h }\] now find the common denominator
anonymous
  • anonymous
so you multiply it by h?
Nnesha
  • Nnesha
first deal with the numerator 2a+2h/a+h-1 + 2a/a-1
anonymous
  • anonymous
what about it
Nnesha
  • Nnesha
what would be the common denominator ?
Nnesha
  • Nnesha
brb i'll login to other laptop
anonymous
  • anonymous
shouldnt it be a+h-1?
Nnesha
  • Nnesha
both denominator are not the same so we should multiply both denominator \[\huge\rm \frac{ (\color{Red}{a-1})(2a+2h) + 2a(\color{blue}{a+h-1}) }{ (a+h-1)(a-1)}\] and when we find common denominator we should multiply numerator of first fraction by the denominator of 2nd fraction
Nnesha
  • Nnesha
and multiply the numerator of 2nd fraction with the denominator of first
anonymous
  • anonymous
so what did get
Nnesha
  • Nnesha
|dw:1443222925608:dw| kinda like cross multiplication
Nnesha
  • Nnesha
now distribute
anonymous
  • anonymous
ok one sec
anonymous
  • anonymous
is a+1 conssidered one term?
Nnesha
  • Nnesha
no term is separated by + or minus sign so two terms
anonymous
  • anonymous
okay i got it
anonymous
  • anonymous
|dw:1443223280971:dw|
anonymous
  • anonymous
am i correct
Nnesha
  • Nnesha
wait a sec
Nnesha
  • Nnesha
|dw:1443223535245:dw| that supposed to be -2a bec 2a times -1 = -2a :=)
Nnesha
  • Nnesha
now combine like terms
Nnesha
  • Nnesha
|dw:1443223669791:dw|
anonymous
  • anonymous
okay
anonymous
  • anonymous
we usually cancel terms out did i miss a minus symbol somewhere
Nnesha
  • Nnesha
ye .. there is a negative sign in the formula that's why i was thinkin why are we getting ugly answer :D
Nnesha
  • Nnesha
\[\huge\rm \frac{ f(x+h) -f(x)}{ h }\] sorry about it
Nnesha
  • Nnesha
|dw:1443224174112:dw|
Nnesha
  • Nnesha
last one is + 2a
Nnesha
  • Nnesha
|dw:1443224257573:dw|
Nnesha
  • Nnesha
\[\huge\rm \frac{\frac{ -2h }{ a^2-a+ah-h-a+1 }}{ h }\] now simplify you can change division to multiplication
Nnesha
  • Nnesha
u there ?? o.O
anonymous
  • anonymous
yes sorry i was rying to work it out
Nnesha
  • Nnesha
oh okay take ur time :)

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