Answer
$x=-4, x=-\frac{1}{4}$
Work Step by Step
$\frac{x+4}{x+1}+\frac{x+4}{3x}=0$
$(x+4)(\frac{1}{x+1}+\frac{1}{3x})=0$
$\frac{(x+4)(3x+x+1)}{(x+1)(3x)}=0$
$\frac{(x+4)(4x+1)}{(x+1)(3x)}=0$
$x=-4, x=-\frac{1}{4}$
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