Home » Simplify (frac{sqrt{2}}{sqrt{3} – sqrt{2}}) – (frac{3 – 2}{sqrt{3} + sqrt{2}})

Simplify (frac{sqrt{2}}{sqrt{3} – sqrt{2}}) – (frac{3 – 2}{sqrt{3} + sqrt{2}})

Simplify (frac{sqrt{2}}{sqrt{3} – sqrt{2}}) – (frac{3 – 2}{sqrt{3} + sqrt{2}})

  • A.
    2(sqrt{2} – sqrt{3})
  • B.
    3((sqrt{6}) – 1)
  • C.
    (sqrt{6}) – 3
  • D.
    -(frac{1}{2})
  • E.
    (frac{-sqrt{3}}{sqrt{2} – sqrt{2}})
Correct Answer: Option B
Explanation

(frac{sqrt{2}}{sqrt{3} – sqrt{2}}) – (frac{3 – 2}{sqrt{3} + sqrt{2}})
(frac{sqrt{2}}{sqrt{3} – sqrt{2}}) = (frac{sqrt{2}}{sqrt{3}}) – (frac{x}{sqrt{2}})
(frac{sqrt{3} + sqrt{2}}{3 + sqrt{2}}) = (sqrt{6}) + 2
(frac{sqrt{3} – sqrt{2}}{sqrt{3} + sqrt{2}}) = (frac{sqrt{3} – sqrt{2}}{sqrt{3} + sqrt{2}}) x (frac{sqrt{3} – sqrt{2}}{sqrt{3} – sqrt{2}})
= 5 – 2(sqrt{6})
(sqrt{6}) + 2 – (5 – 2 (sqrt{6})) = (sqrt{6}) + 2 – 5 + 2(sqrt{6})
= 3(sqrt{6}) – 3
= 3((sqrt{6}) – 1)