Question

rationalize the denominator 1/(1+√5+√3)

Answer 1

$\frac{1}{1 + \sqrt{5} + \sqrt{3} } \\ = \frac{(1 + \sqrt{5}) - \sqrt{3} }{((1 + \sqrt{5}) + \sqrt{3} ) \times ((1 + \sqrt{5}) - \sqrt{3} ) } \\ = \frac{(1 + \sqrt{5}) - \sqrt{3} }{((1 + \sqrt{5}) + \sqrt{3} ) \times ((1 + \sqrt{5}) - \sqrt{3} ) } \\ = \frac{(1 + \sqrt{5} ) - \sqrt{3} }{( {1 + \sqrt{5} )}^{2} - ( { \sqrt{3} }^{2}) } \\ = \frac{1 + \sqrt{5} - \sqrt{3} }{1 + 5 + 2 \sqrt{5} - 3} \\ = \frac{1 + \sqrt{5} - \sqrt{3} }{3 + 2 \sqrt{5} } \\ = \frac{(1 + \sqrt{5} - \sqrt{3})(3 - 2 \sqrt{5} )}{(3 + 2 \sqrt{5} )(3 - 2 \sqrt{5}) } \\ = \frac{3 - 2 \sqrt{5} + 3 \sqrt{5} - 10 - 3 \sqrt{3} + 2 \sqrt{15} }{9 - 20} \\ = \frac{ - 7 + \sqrt{5} - 3 \sqrt{3} + 2 \sqrt{15} }{ - 11} \\ = \frac{7 - \sqrt{5} + 3 \sqrt{3} - 2 \sqrt{15} }{ 11}$

Answer 2

Step-by-step explanation:

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