Question

$\frac{ \sqrt{3} + 1}{ \sqrt{3} - 1} = a + b \sqrt{3}$
Find the value of a and b
please help me with explanation​

Answer 1

(√3+1 ) / (√3 - 1) = [(√3+1)(√3-1)] / [(√3-1)^2]

[(√3-1)^2] = [(√3)^2 - 1^2] / [(√3)^2 - 2√3 +1]

=[ 3 - 1] / [3 - 2√3 +1 ]

= 2 / (4 - 2√3)

= 1 / (2 - √3)

= (2+√3) /[ ( 2-√3 ) ( 2 + √3)

= (2+√3) /[( 2^2 - √3^2 )

= (2+√3) / (4 - 3 )

= (2 + √3) / 1

= 2 + √3

2 + √3 = a + b√3

a = 2

b = 1