Question

√3+1/√3-1=a+b√3 ......

Answer 1

heya mate here is your answer

$\frac{ \sqrt{3} + 1}{ \sqrt{3} - 1 } = a + b \sqrt{3}$

(√3+1)(√3+1)/(√3-1)(√3+1) [rationalising the denominator]

(√3+1)² / (√3)²-(1)²

3+2√3+1 / 3-1

4+3√3 /2 = 2(2+√3) / 2

$2 + \sqrt{3} = a + b \sqrt{3}$

so here a = 2 and b = 1

hope it helps