45/x+3  24/x = 1
Thanks in advance

ConorTh
any questions just ask!

ConorTh
picture should be attached

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 = (x6)(x12)
Factor therom to get roots: x = 6 and x = 12

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

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:
(x6)(x12) = 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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