Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    1
    ReputationRep:
    (x-1)/(x^2-1) = (x-1)/(x-1).(x+1) = 1/(x+1)

    If I set x = 1, then why does (x-1)/(x^2-1) = 0/0

    but 1/(x+1) = 1/2
    Offline

    13
    ReputationRep:
    (x-1)/(x^2-1) isn't defined at x=1 but the limit as x tends to 1 exists and is 1/2
    Offline

    0
    ReputationRep:
    mind = blown
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by SsEe)
    (x-1)/(x^2-1) isn't defined at x=1 but the limit as x tends to 1 exists and is 1/2
    so x=1 isnt defined at (x-1)/(x^2-1)

    but x =1 is defined at 1/(x+1)

    despite the fact that (x-1)/(x^2-1) = 1/(x+1)
    Offline

    0
    ReputationRep:
    (Original post by StadtJunky)
    so x=1 isnt defined at (x-1)/(x^2-1)

    but x =1 is defined at 1/(x+1)

    despite the fact that (x-1)/(x^2-1) = 1/(x+1)
    If you are talking about graphs, and geometrically representing these as functions, then I don't think you can say that

    \displaystyle \frac{(x-1)}{(x^2-1)} = \frac{1}{(x+1)}

    While elementary algebra gives an apparent equivalence between the two, geometrical and algebraic forms are still separate representations, and care must be taken converting from one form to the other.

    If you want one way of thinking about it, the algebraic manipulation you have gone through is simply a way of 'ignoring' the presence of the asymptote. Try plotting both graphs and comparing their shapes, maybe.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by james.h)
    If you are talking about graphs, and geometrically representing these as functions, then I don't think you can say that

    \displaystyle \frac{(x-1)}{(x^2-1)} = \frac{1}{(x+1)}

    While elementary algebra gives an apparent equivalence between the two, geometrical and algebraic forms are still separate representations, and care must be taken converting from one form to the other.

    If you want one way of thinking about it, the algebraic manipulation you have gone through is simply a way of 'ignoring' the presence of the asymptote. Try plotting both graphs and comparing their shapes, maybe.
    They have identical shapes...
    Offline

    13
    ReputationRep:
    (Original post by StadtJunky)
    so x=1 isnt defined at (x-1)/(x^2-1)

    but x =1 is defined at 1/(x+1)

    despite the fact that (x-1)/(x^2-1) = 1/(x+1)
    Both are defined and equal everywhere except x=1 and x=-1. At x=-1, neither are defined. At x=1, the former is not defined (but has a limit as x tends to 1) and the latter is defined. So really, they're not strictly identical.
    Offline

    1
    ReputationRep:
    You have kind of divided by (x-1), which when x=1 is 0, which isn't allowed. Naughty :p:
    Offline

    0
    ReputationRep:
    (Original post by MathsHamster)
    You have kind of divided by (x-1), which when x=1 is 0, which isn't allowed. Naughty :p:
    Ha! Can't believe I missed that. :o: :getmecoat:
    Offline

    0
    ReputationRep:
    (Original post by MathsHamster)
    You have kind of divided by (x-1), which when x=1 is 0, which isn't allowed. Naughty :p:
    :facepalm:
    • Wiki Support Team
    Offline

    14
    ReputationRep:
    Wiki Support Team
    (Original post by StadtJunky)
    (x-1)/(x^2-1) = 1/(x+1)
    This isn't true. It's "almost" true, in various very specific and technical senses, but it's not actually true, because (as you said yourself) the left hand side isn't quite defined at x = 1 (it is trivially easy to work out how you'd like to define it there, but it is not defined there by default, because the actual theory behind showing you can do so isn't easy), and the right hand side is. They behave identically everywhere else.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Has a teacher ever helped you cheat?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.