Step-by-step explanation:
[tex]a - \frac{1}{a} \\ \frac{ {a}^{2} - 1 }{a} \\ = \frac{ {(2 + \sqrt{3} )}^{2} - 1}{2 + \sqrt{3} } \\ = \frac{7 + 4 \sqrt{3} - 1 }{2 + \sqrt{3} } = \frac{6 + 4 \sqrt{3} }{2 + \sqrt{3} } = 2 \sqrt{3} [/tex]
