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anonymous

  • one year ago

find the difference quotient of f(x)= (2x)/(x-1)

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  1. anonymous
    • one year ago
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    @Nnesha can you please help me

  2. Nnesha
    • one year ago
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    we need to use formula f(x+h)-f(x) over h right ?

  3. anonymous
    • one year ago
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    instead of x im using a but yes

  4. anonymous
    • one year ago
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    f(a)= (2a)/(a-1)

  5. Nnesha
    • one year ago
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    ohh okay so first we have to find f(a+h) substitute a for a+h

  6. anonymous
    • one year ago
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    and f(a+h)= (2a+2h)/(-a-h)

  7. anonymous
    • one year ago
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    am i correct

  8. Nnesha
    • one year ago
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    the denominator would be a-1 = (a+h)-1 so it would be a+h-1 it's not a multiplication

  9. anonymous
    • one year ago
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    oh alright

  10. Nnesha
    • one year ago
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    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

  11. anonymous
    • one year ago
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    so you multiply it by h?

  12. Nnesha
    • one year ago
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    first deal with the numerator 2a+2h/a+h-1 + 2a/a-1

  13. anonymous
    • one year ago
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    what about it

  14. Nnesha
    • one year ago
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    what would be the common denominator ?

  15. Nnesha
    • one year ago
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    brb i'll login to other laptop

  16. anonymous
    • one year ago
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    shouldnt it be a+h-1?

  17. Nnesha
    • one year ago
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    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

  18. Nnesha
    • one year ago
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    and multiply the numerator of 2nd fraction with the denominator of first

  19. anonymous
    • one year ago
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    so what did get

  20. Nnesha
    • one year ago
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    |dw:1443222925608:dw| kinda like cross multiplication

  21. Nnesha
    • one year ago
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    now distribute

  22. anonymous
    • one year ago
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    ok one sec

  23. anonymous
    • one year ago
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    is a+1 conssidered one term?

  24. Nnesha
    • one year ago
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    no term is separated by + or minus sign so two terms

  25. anonymous
    • one year ago
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    okay i got it

  26. anonymous
    • one year ago
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    |dw:1443223280971:dw|

  27. anonymous
    • one year ago
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    am i correct

  28. Nnesha
    • one year ago
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    wait a sec

  29. Nnesha
    • one year ago
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    |dw:1443223535245:dw| that supposed to be -2a bec 2a times -1 = -2a :=)

  30. Nnesha
    • one year ago
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    now combine like terms

  31. Nnesha
    • one year ago
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    |dw:1443223669791:dw|

  32. anonymous
    • one year ago
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    okay

  33. anonymous
    • one year ago
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    we usually cancel terms out did i miss a minus symbol somewhere

  34. Nnesha
    • one year ago
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    ye .. there is a negative sign in the formula that's why i was thinkin why are we getting ugly answer :D

  35. Nnesha
    • one year ago
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    \[\huge\rm \frac{ f(x+h) -f(x)}{ h }\] sorry about it

  36. Nnesha
    • one year ago
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    |dw:1443224174112:dw|

  37. Nnesha
    • one year ago
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    last one is + 2a

  38. Nnesha
    • one year ago
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    |dw:1443224257573:dw|

  39. Nnesha
    • one year ago
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    \[\huge\rm \frac{\frac{ -2h }{ a^2-a+ah-h-a+1 }}{ h }\] now simplify you can change division to multiplication

  40. Nnesha
    • one year ago
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    u there ?? o.O

  41. anonymous
    • one year ago
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    yes sorry i was rying to work it out

  42. Nnesha
    • one year ago
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    oh okay take ur time :)

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