Answer:

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step by step explanation:

Given √3-1 /√3+1 = a+b√3

First let us rationalize the denominator

of √3-1 /√3+1

Multiplying numerator and denominator

by √3-1, we get

= √3-1 /√3+1 x √3-1/ √3-1

= 3-√3-√3+1/ (√3)²- (1)² [Since,

(a+b)(a - b) = a² - b²]

=3-2√3+1/3-1

= 4-2√3 /2

=2(2-√3)/2

=2-√3

Thus, given expression can be rewritten as

2-√3 = a+b√3

then by principle of homoginity.

We have a = 2 and b = -1