Question

rationalize the denominator
√3+1
______
√3-1​

Answer 1

$\bf\underbrace\red{answer:}$

identities used are

(a+b) ² = a²+b²+2ab

(a+b) (a-b) =a²-b²

$\\ \frac{ \sqrt{3 + 1} }{ \sqrt{3 - 1} } \\ = \frac{ \sqrt{3 + 1} }{ \sqrt{3 - 1} } \times \frac{ \sqrt{3 + 1} }{ \sqrt{3 + 1} } \\ \frac{ \sqrt{3} + \sqrt{1} )^{2} }{( \sqrt{3 )^{2} - 1 } } \\ = \frac{3 + 1 + 2 \sqrt{3} }{2} \\ = \frac{4 + 2 \sqrt{3} }{2} \\ = \frac{2(2 + \sqrt{3)} }{2} \\ = 2 + \sqrt{3} \: \: answer$

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