3/x+5/3x=1
9x+5x=1
14x=1
x=-13
is this right
Did you mean
3/x + (5/3)x = 1 the way you typed it, or
3/x + 5/(3x) = 1
I will solve it the way you typed it
multiply each term by 3x
9 + 5x^2 = 3x
5x^2 - 3x + 9 = 0
This quadratic has no solution
if you meant 3/x + 5/(3x) = 1
multiply each term by 3x
9 + 5 = 3x
3x = 14
x = 14/3
Your solution does not follow either of the interpretations.
You did something mysterious to the left side, but did not do it to the right side.