Multiple choice general knowledge math & puzzles

Which of the following is equal to the reciprocal of (4 + (thesquare root of 15))?

  1. (1/4) + (the square root of 15)/15

  2. 4 - (the square root of 15)

  3. (1/4) - (the square root of 15)/15

  4. 1/4) + (the square root of 15)/4
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B Correct answer
Explanation

1/(4 + √15) rationalizes by multiplying numerator and denominator by the conjugate (4 - √15): [1 × (4 - √15)] / [(4 + √15)(4 - √15)] = (4 - √15) / (16 - 15) = (4 - √15) / 1 = 4 - √15. Rationalizing denominators eliminates radicals from fractions.

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