Question 119463
The given expression is: 


{{{(4/(x-1)) + (6/(3x+1)) = (15/(3x+1))}}}


Taking LCD, we get:


{{{(4(3x + 1) + 6(x - 1))/(x - 1)(3x + 1)}}} = {{{(15/(3x + 1))}}}



{{{(12x + 4 + 6x - 6)/(x - 1)(3x + 1)}}} = {{{(15/(3x + 1))}}}


{{{(18x - 2)/(x - 1)(3x + 1)}}} = {{{(15/(3x + 1))}}}



Cross - Multiply: 


{{{((18x - 2)(3x - 1))/(x - 1)(3x + 1)}}} = 15


{{{(18x - 2) = 15(x - 1)}}}


18x - 2 = 15x - 15 


18x - 15x = -15 + 2 


3x = -13


{{{x = -13/3}}}


hence the solution