Answer
No solution.
Work Step by Step
$\displaystyle \frac{3}{x+4}=\frac{1}{x}+\frac{6x+12}{x^{2}+4x}$
We multiply both sides by $x(x+4)$:
$3(x)=(x+4)+6x+12$
Then we distribute:
$3x=7x+16$
And combine $x$ terms:
$-4x=16$
And solve for $x$:
However, if we use $x=-4$ in the original equation, we get division by 0, which is undefined. Therefore there is no solution.
