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Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Why can't x-2/x-6 simplify to 1/3?

12 Answers

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  • 1 month ago

    Because (x-2).(x-6) = 1/3 ONLY if x = 0

  • 2 months ago

    x-2/x-6

    x - (2/x) - 6

    wherever did you get 1/3 ?

  • 2 months ago

    1/3 =

    1/3 * (x - 2)/(x - 2) =

    1(x - 2)/(3(x - 2)) =

    (x - 2)/(3x - 6), not (x - 2)/(x - 6)

  • 2 months ago

    Is x - (2/x) - 6 the same as 1/3? It depends on the value of x.

    x - (2/x) - 6 = 1/3

    Multiply through by 3x:

    3x^2 - 6 - 18x = x

    3x^2 - 18x - 6 - x = 0

    3x^2 - 19x - 6 = 0

    x = (-(-19) +/- sqrt((-19)^2 - 4(3)(-6))) / (2*3)

    x = (19 +/- sqrt(361 + 72)) / 6

    x = (19 +/- sqrt(433)) / 6

    x =~ 6.6347753411141352717951502536839 or -0.30144200778080193846181692035056

    So if x is one of those two values, then yes, you can simplify like that, but otherwise, no.

    Or did you mean:

    (x - 2) / (x - 6) = 1/3

    Cross-multiply:

    3(x - 2) = x - 6

    3x - 6 = x - 6

    3x - 6 - x + 6 = 0

    2x = 0

    x = 0/2

    x = 0

    So if x = 0, then yes, you can simplify like that, but otherwise, no.

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  • 2 months ago

    x - 2 and x - 6 are not  common factors and cannot be equal to 1/3..

  • 2 months ago

    Let x = 4 

    Hence 

    (4 - 2)/(4 - 6) = 

    2/2 = 1 

    This is just an example of using a non-zero number to show that (x -2)/(x -6) is no simply '1/3'. 

  • ?
    Lv 7
    2 months ago

    Assuming this is (x - 2) / (x - 6), x - 2 is one expression by itself and shares no common and cancellable factors with x - 6.  However, if x = 0, the entire rational expression will equal 1/3 ((0 - 2) / (0 - 6) = -2 / -6 = 1/3).

  • Jim
    Lv 7
    2 months ago

    Assuming you meant (x-2)/(x-6)

    let's try one example to disprove it's 1/3:

    If x = 2, then

    (2-2)/(2-6) = 0, so you know for sure it's not 1/3

    In fact, it's 1/3 for only where x=0, all other values it's some other value.

    Attachment image
  • 2 months ago

    (x - 2) / (x - 6)

    Because x isn't a factor so you can't just divide both sides by it to cancel them out.

    That's like saying:

    8 / 4

    and you want to cancel out a 10 (x = 10 from your example).

    That doesn't work.

  • 2 months ago

    (x - 2)/(x - 6)

    = x/(x - 6) - 2/(x - 6)

    Root:

    x = 2

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