[tex]x+1=x\sqrt{3} \\x-x\sqrt{3} =-1\\x(1-\sqrt{3})=-1\\x=\frac{-1}{1-\sqrt{3} } \\x=\frac{-(1+\sqrt{3)} }{(1-\sqrt{3})(1+\sqrt{3} )} \\x=\frac{-(1+\sqrt{3} )}{1-3} \\x=\frac{-(1+\sqrt{3} )}{-2} \\x=\frac{1+\sqrt{3} }{2}[/tex]
[tex]x+1=x\sqrt3\\x-x\sqrt3=-1\\x(1-\sqrt3)=-1\\x=-\dfrac{1}{1-\sqrt3}=-\dfrac{1+\sqrt3}{1-3}=-\dfrac{1+\sqrt3}{-2}=\dfrac{1+\sqrt3}{2}[/tex]
