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\left(3\sqrt{3}+3\right)x=\sqrt{3}+1
The equation is in standard form.
\frac{\left(3\sqrt{3}+3\right)x}{3\sqrt{3}+3}=\frac{\sqrt{3}+1}{3\sqrt{3}+3}
Divide both sides by 3+3\sqrt{3}.
x=\frac{\sqrt{3}+1}{3\sqrt{3}+3}
Dividing by 3+3\sqrt{3} undoes the multiplication by 3+3\sqrt{3}.
x=\frac{1}{3}
Divide 1+\sqrt{3} by 3+3\sqrt{3}.