Question 190905
 the problem is {{{((x-1))/x}}} + {{{7/(3x)}}} = {{{9/(4x)}}}
I think you are right but let's just go thru it and check the solution
12x*{{{((x-1))/x}}} + 12x*{{{7/(3x)}}} = 12x*{{{9/(4x)}}}
Cancel out the denominators and you have:
12(x-1) + 4(7) = 3(9)
12x - 12 + 28 = 27
12x + 16 = 27
12x = 27 - 16
12x = 11
x = {{{11/12}}} just as you said
:
:
But you can be sure by substituting 11/12 for x in the original problem:
{{{((x-1))/x}}} + {{{7/(3x)}}} = {{{9/(4x)}}}
Remember when you have a fraction in the denominator, you invert it and mult
the numerator: 
((11/12) - 1)*(12/11)) + 7(12/33) = 9(12/44)
:
((-1/12)*(12/11)) + 7(12/33) = 9(12/44)
;
(-1/11) + (84/33) = (108/44)
;
Reduce the fractions
(-1/11) + (28/11) = (27/11); confirms our solution