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if a = 4/3-root5 find the value of a+4/a

$g i v e n : a = \frac{4}{3 - \sqrt{5}} n o w, a + \frac{4}{a} = \frac{4}{3 - \sqrt{5}} + \frac{4}{\frac{4}{3 - \sqrt{5}}} = \frac{4}{3 - \sqrt{5}} + \frac{4 (3 - \sqrt{5})}{4} = \frac{4}{3 - \sqrt{5}} + 3 - \sqrt{5} = \frac{4 + 9 + 5 - 6 \sqrt{5}}{3 - \sqrt{5}} = \frac{18 - 6 \sqrt{5}}{3 - \sqrt{5}} = \frac{6 (3 - \sqrt{5})}{3 - \sqrt{5}} = 6$

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