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45/x+3 - 24/x = 1

2. #### ConorTh

picture should be attached

3. #### 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. #### 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

5. #### 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

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 :)