Question

please solve this and the answer is
$2 + \sqrt{3}$


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Answer 1

Step-by-step explanation:

$\frac{ \sqrt{3} + 1 }{ \sqrt{3} - 1}$

$\frac{ (\sqrt{3} + 1) \times ( \sqrt{3} + 1)}{2}$

$\frac{( \sqrt{3} + 1) {}^{2} }{2}$

$\frac{3 + 2 \sqrt{3} + 1}{2}$

$\frac{4 + 2 \sqrt{3} }{2}$

$\frac{2(2 + \sqrt{3}) }{2}$

$2 + \sqrt{3}$

Please Marked me as brainly

Answer 2

Answer:

Step-by-step explanation:

√3+1/√3-1

RATIONALISING THE DENOMINATOR

MULTIPLYING BOTH NUMERATOR AND DENOMINATOR BY √3+1

= (√3+1)(√3+1)/(√3-1)(√3+1)

= (√3+1)²/(√3-1)(√3+1)

THE DENOMINATOR IS OF THE FORM (A+B)(A-B) = A²-B²

THE NUMERATOR COULD BE EXPANDED USING :

(A+B)²= A²+B²+2*A*B

= [(√3)²+(1)²+2*√3*1]/[(√3)²-(1)²]

= [ 3+1+2√3]/3-1

= (4+2√3)/2

TAKING TWO COMMON OUTSIDE.

= 2(2+√3)/2

= 2+√3.

HOPE THIS HELPS.