Mathematics

Question

I'm completely lost on this question please help
I'm completely lost on this question please help

2 Answer

  • first, note that y≠0 and y≠4 because that would make the denomenators 0 which is undefined

     
    we got to get rid of fractions
    common denomenator is y(y-4)
    multiply both sides by y(y-4)
    2y+y-4=y(y-1)
    3y-4=y²-y
    minus 3y both sides
    -4=y²-4y
    add 4 both sides
    0=y²-4y+4
    factor
    what 2 numbers multiply to get 4 and add to get -4?
    -2 and -2
    0=(y-2)(y-2)
    set to zero

    y-2=0
    y=2
    no extranious roots


    y=2 is the solution
  • Multiply the numerators by "y" which yields:
    (2y) / (y-4)  +1 = (y^2 -y) / (y-4)
    (2y) / (y-4)  - (y^2 -y) / (y-4) = -1

    (2y) - (y^2 -y) / (y-4) = -1

    (2y) - (y^2 -y) = -y +1

    -y^2 +2y -y +y = 1

    -y^2 +2y -1 = 0

    Multiplying by -1

    y^2 -2y +1 = 0

    (y -1) * (y - 1) = 0

    x = 1
    x= 1

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