Question 135704
Given : {{{(3x)/(x+1) + 6/(2X) = 7/x }}} 
{{{(3x)/(x+1) + 6/(2X) - 7/x = 0}}} 

now look in the current denominators and see what unique factors are there.
We have {{{(x+1)}}} and {{{2x}}} the other solitary x is already covered by the {{{2x}}}.

So

{{{(3x*2x)/((2x)*(x+1)) + (6*(x+1))/((2x)*(x+1)) - ((7)*(2)*(x+1))/((2x)*(x+1)) = 0}}}
{{{(6x^2 + 6x+6 - 14x - 14)/((2x)*(x+1)) = 0}}}
{{{(6x^2 -8x -8)/((2x)*(x+1)) = 0}}}
{{{6x^2 - 8x - 8}}} = 0
Use the quadratic equation to solve. Then check your answers to make sure that the values of x given do not make {{{((2x)*(x+1))}}} = 0 too