Question 119584
1. 9/x = 4/3x + 1 
:
Assume you mean:
{{{9/x}}} = {{{4/3}}}x + 1
:
Multiply equation by 3x to get rid of the denominators:
3x*{{{9/x}}} = 3x*{{{4/3}}}x + 3x(1)
:
Cancel out the denominators and you have:
3(9) = x(4x) + 3x
27 = 4x^2 + 3x
:
Arrange as a quadratic equation:
4x^2 + 3x - 27 = 0
:
Factor this to:
(x + 3)(4x - 9) = 0
Two solutions
x = -3
and 
4x = +9
x = {{{9/4}}}
x = 2.25
;
:
Check solution in original equation using x = +2.25:
{{{9/2.25}}} = {{{4/3}}}2.25 + 1
  4 = 3 + 1:; confirms our solutlio
:
You can check the x = -3 solution
:
:
If I have misinterpreted this problem, it's {{{9/x}}} = {{{4/(3x)}}} + 1
then this is a whole difference animal and will have to be done over.
Let me know.