Home » simplify (frac{1}{√3 – 2}) – (frac{1}{√3 + 2})

simplify (frac{1}{√3 – 2}) – (frac{1}{√3 + 2})

simplify (frac{1}{√3 – 2}) – (frac{1}{√3 + 2})
  • A.
    3
  • B.
    (frac{2}{3})
  • C.
    7
  • D.
    -4
Correct Answer: Option D
Explanation

(frac{1}{√3 – 2}) – (frac{1}{√3 + 2})
L.C.M = (3- 2) (3 + 2)
∴ (frac{1}{sqrt{3 – 2}}) – (frac{1}{sqrt{3 – 2}}) = (frac{sqrt{3 + 2} – sqrt{3 – 2}}{sqrt{3 – 2} + sqrt{3 – 2}})
(frac{√3 + 2 – √3 + 2}{3 – 2√3 + 2√3 – 4}) = (frac{4}{3 – 2})
= (frac{4}{-1})
= -4

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