College Algebra (6th Edition)

$x=-1$
$y=\dfrac{x+6}{3x-12}-\dfrac{5}{x-4}-\dfrac{2}{3}$ Set $y$ equal to $0$: $\dfrac{x+6}{3x-12}-\dfrac{5}{x-4}-\dfrac{2}{3}=0$ Factor the denominator of the first fraction: $\dfrac{x+6}{3(x-4)}-\dfrac{5}{x-4}-\dfrac{2}{3}=0$ Multiply the whole equation by $3(x-4)$: $3(x-4)\Big[\dfrac{x+6}{3(x-4)}-\dfrac{5}{x-4}-\dfrac{2}{3}=0\Big]$ $(x+6)-(5)(3)-2(x-4)=0$ $x+6-15-2x+8=0$ Take all terms without $x$ to the right side, simplify and solve for $x$: $x-2x=-8-6+15$ $-x=1$ $x=-1$