If x = √3 + √2, then the value of (x + 1)/(x

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If x = √3 + √2, then the value of (x + 1)/(x - 1) - (x - 1)/(x + 1) is ?

1. √3
2. √2
3. √6
4. None of above

Correct Option: B

(x + 1)/(x - 1) - (x - 1)/(x + 1) = {(x + 1)² - (x - 1)²} / {(x - 1) (x + 1)}
= (x² + 1 + 2x) - (x² + 1 - 2x) / (x² - 1)
= 4x / (x² - 1) = 4(√3 + √2) / {(√3 + √2)² - 1}
= 4(√3 + √2) / (3 + 2 + 2√6 - 1) = 4(√3 + √2) / (4 + 2 √6)
= 4(√3 + √2) / 2 √2 (√3 + √2)
= √2