5/X - 2/3X = 17 1/3
Yes, you're right; the best thing to do would be to turn 17 1/3 into the fraction 52/3.
Then the easiest way to continue is probably to multiply both sides of the equation by X:
5 - (2/3) = (52/3)X
Then put the left hand side of the equation over the same denominator:
5x(3/3) - (2/3) = (52/3)X
(5x3)/3 - (2/3) = (52/3)X
15/3 - 2/3 = (52/3)X
(15-2)/3 = (52/3)X
13/3 = (52/3)X
Then multiply both sides of the equation by 3:
13 = 52X
Then divide both sides by 52,
So, X = 13/52
This can then be simplified:
So, X = (13/13)/(52/13)
X = 1/4