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\frac{\left(\sqrt{3}+1\right)b}{\sqrt{3}+1}=\frac{4}{\sqrt{3}+1}
Divide both sides by \sqrt{3}+1.
b=\frac{4}{\sqrt{3}+1}
Dividing by \sqrt{3}+1 undoes the multiplication by \sqrt{3}+1.
b=2\sqrt{3}-2
Divide 4 by \sqrt{3}+1.