If [√3 + x + √3 - x] / [√3 + x

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If [√3 + x + √3 - x] / [√3 + x - √3 - x] = 2, then x is equal to

1. 5/12
2. 12/5
3. 5/7
4. 7/5

Correct Option: B

[√3 + x + √3 - x] / [√3 + x - √3 - x] = 2

Let √3 + x = a and √3 - x = b
Then, (a + b) / (a - b) = 2/1
∴ a + b = 2a - 2b
⇒ a = 3b

∴ √3 + x = 3√3 - x

On squaring bothv sides, we get
(√3 + x)² = (3√3 - x)²
⇒ 3 + x = 9(3 - x)
⇒ 3 + x = 27 - 9x
⇒ 10x = 24
∴ x = 12/5