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2+root3/2-root3 + 2-root3/2+root3 + root3-1/root3+1=a+b root3 find the rational numbers a and b

$Given \frac{2 + \sqrt{3}}{2 - \sqrt{3}} + \frac{2 - \sqrt{3}}{2 + \sqrt{3}} + \frac{\sqrt{3} - 1}{\sqrt{3} + 1} \Rightarrow \frac{2 + \sqrt{3}}{2 - \sqrt{3}} \times \frac{2 + \sqrt{3}}{2 + \sqrt{3}} + \frac{2 - \sqrt{3}}{2 + \sqrt{3}} \times \frac{2 - \sqrt{3}}{2 - \sqrt{3}} + \frac{\sqrt{3} - 1}{\sqrt{3} + 1} \times \frac{\sqrt{3} - 1}{\sqrt{3} - 1} \Rightarrow \frac{4 + 3 + 4 \sqrt{3}}{4 - 3} + \frac{4 + 3 - 4 \sqrt{3}}{4 - 3} + \frac{3 + 1 - 2 \sqrt{3}}{3 - 1} \Rightarrow 14 + \frac{4 - 2 \sqrt{3}}{2} \Rightarrow 14 + 2 - \sqrt{3} \Rightarrow 16 - \sqrt{3} = a + b \sqrt{3} \Rightarrow a = 16 b = - 1$

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