If `(sqrt(3)-\ 1)/(sqrt(3)+\ 1)=a-b\ sqrt(3)` , then `a=2,\ b=1` (b) `a=2,\ b=-1` `a=-2,\ b=1` (d) `a=b=1`

Explanation

To solve the equation \(\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = a - b\sqrt{3}\), we will rationalize the left-hand side.

### Step 1: Rationalize the Expression
We will multiply both the numerator and the denominator by the conjugate of the denominator, which is \(\sqrt{3} - 1\).

\[ \frac{\sqrt{3} - 1}{\sqrt{3} + 1} \cdot \frac{\sqrt{3} - 1}{\sqrt{3} - 1} = \frac{(\sqrt{3} - 1)^2}{(\sqrt{3} + 1)(\sqrt{3} - 1)} \]
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