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    Solve please djsutt0n

    45/x+3 - 24/x = 1

    Thanks in advance

    1. avatar image

      ConorTh

      any questions just ask!

    2. avatar image

      ConorTh

      picture should be attached

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      ConorTh

      well ... apparently not.

      Ok well

      45/x+3 - 24/x = 1

      bring your - 24/x over the other side and you get 45/x+3 = 1 + 24/x

      now multiply 1 by x top and bottom (as 1 is 1/1) in order to have the same denominator. Now bring them together and you get 45/x+3 = 24+x/x

      Cross multiply giving you 45x = (24+x)(x+3)

      multiply that out and get 45x = 24x +72 + x^2 + 3x

      simplify and let equal 0 to get: x^2 - 18x + 72

      Solve by factorising: Factors = (x-6)(x-12)

      Factor therom to get roots: x = 6 and x = 12

    4. avatar image

      themathstutor.ie

      Is the first term really 45/x or is it 45/(x+3) ?

      I would guess 45/(x+3). In that case Conor's values for x are correct, you can check by subbing them in.

      Conor, you also need to be careful to use brackets:

      45/x+3 = 24+x/x in your 5th line

      should be

      45/(x+3) = (24+x)/x

      [Note that if the first term is 45/x as you seem to imply, with the +3 as a separate term, then it's a different function and a different solution. But I guess it's just a typo?]

      Eamonn - TheMathsTutor.ie

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      Dazzla16

      Hi djsutt0n! I have a similar worked answer as ConorTh, but it has a slight difference:

      45/(x+3) - 24/x = 1

      Multiply both sides by x:

      45x/(x+3) - 24 = x

      Add 24 to both sides:

      45x/(x+3) = x + 24

      Multiply both sides by (x+3):

      45x = (x+3)(x+24)

      45x = x^2 + 24x + 3x + 72

      45x = x^2 + 27x + 72

      Subtract 45x from both sides:

      0 = x^2 + 27x + 72 - 45x

      0 = x^2 - 18x + 72

      x^2 - 18x + 72 = 0

      Factorise one side by trinomials:

      (x-6)(x-12) = 0

      Let each factor equal 0:

      x - 6 = 0 or x - 12 = 0

      x = 6 or x = 12

      Hope it helps :)

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