Question 771303
This same question has just been asked four times under different categories.  

The three summed expression use these completely factored denominators:

(1)_______ {{{(x+6)}}}
(2)_______ {{{3*(x+6)}}}
(3)_______ {{{4*(x+6)}}}


You want the simplest or "least" common multiple for all of those three expressions.  The x+6 occurs ONE time at most in any of the expression.
The 3 occurs at most ONE time in any of the expressions.
The 4 occurs at most ONE time in any of the expressions.

The lowest common multiple, is then {{{highlight(3*4*(x+6))}}} or in fully multiplied form, {{{highlight(12x+72)}}}



SOLVING THE EQUATION


Multiply both sides by 12x+72.
{{{(12x+72)(8/(x+6) + 1/(3x+18) - 14/(4x+24)) = 0(12x+72)}}}
{{{12*8+12-12*14=0}}}
{{{12*8-12*14+12=0}}}
{{{12(8-14+1)=0}}}
{{{12*(-5)=0}}}
{{{highlight(-60=0)}}} FALSE STATEMENT!
The given equation has no solution.