Question

(√3-1)x-3=2x(√3+1)-3√3

Answer 1

[tex](\sqrt3-1)x-3=2x(\sqrt3+1)-3\sqrt3\\ (\sqrt3-1)x-3+3\sqrt3=2x(\sqrt3+1)\\ (\sqrt3-1)x+3(\sqrt3-1)=2x(\sqrt3+1)\\ (\sqrt3-1)(x+3)=2x(\sqrt3+1)\\ \frac{x+3}{2x}=\frac{\sqrt3+1}{\sqrt3-1}\\ \frac{x+3}{2x}=\frac{(\sqrt3+1)^2}{(\sqrt3-1)(\sqrt3+1)}\\ \frac{x+3}{2x}=\frac{3+1+2\sqrt3}{3-1}\\ \frac{x+3}{2x}=\frac{2(2+\sqrt3)}{2}\\ \frac{x+3}{2x}=2+\sqrt3\\ x+3=x(4+2\sqrt3)\\ x(4+2\sqrt3-1)=3\\ x(3+2\sqrt3)=3\\ x=\frac{3}{3+2\sqrt3}\\ x=\frac{3(2\sqrt3 -3)}{(2\sqrt3+3)(2\sqrt3-3)}\\ [/tex]
[tex]x=\frac{3(2\sqrt3-3)}{12-9}\\ x=\frac{3(2\sqrt3-3)}{3}\\ x=2\sqrt3-3[/tex]