Question

solve this question fast​

Answer 1

Step-by-step explanation:

To rationalize we will multiply and divide the denominator by √3+1

(√3+1)√3+1)/(√3-1)(√3+1)

Denominator can be simplified using the identity (a2-b2)=(a-b)(a+b)

And the equation becomes

=(√3+1)2/(√3)2-(1)2

=(4+2√3)/2

=2+√3

Answer 2

Answer:

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

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