[tex]\displaystyle \left| \frac{x-1}{x+ \sqrt{3} } \right|=2 \\ \\ \frac{x-1}{x+ \sqrt{3} } =2 \\ x-1=2(x+ \sqrt{3} ) \\ x-1=2x+2 \sqrt{3} \\ x-2x=2 \sqrt{3} +1 \\ -x=2 \sqrt{3} +1 \\ -x=-2 \sqrt{3} -1 \\ \frac{x-1}{x+ \sqrt{3} }=-2 \\ \\ x-1=-2(x+ \sqrt{3} ) \\ x-1=-2x-2 \sqrt{3} \\ x+2x=-2 \sqrt{3}+1 \\ 3x=-2 \sqrt{3} +1 \\ x= \frac{-2 \sqrt{3} +1}{3} [/tex]
