Home » Simplify (frac{sqrt{1 + x} + sqrt{x}}{sqrt{1 + x} – sqrt{x}})

Simplify (frac{sqrt{1 + x} + sqrt{x}}{sqrt{1 + x} – sqrt{x}})

Simplify (frac{sqrt{1 + x} + sqrt{x}}{sqrt{1 + x} – sqrt{x}})

  • A.
    -2x – 2(sqrt{x (1 + x)})
  • B.
    1 + 2x + 2(sqrt{x (1 + x)})
  • C.
    (sqrt{x (1 + x)})
  • D.
    1 + 2x – 2(sqrt{x (1 + x)})
Correct Answer: Option B
Explanation

(frac{sqrt{1 + x} + sqrt{x}}{sqrt{1 + x} – sqrt{x}})

= ((frac{sqrt{1 + x} + sqrt{x}}{sqrt{1 + x} – sqrt{x}}) (frac{sqrt{1 + x} + sqrt{x}}{sqrt{1 + x} + sqrt{x}}))

= (frac{(1 + x) + sqrt{x(1 + x)} + sqrt{x(1 + x)} + x}{(1 + x) – x})

= (frac{1 + 2x + 2sqrt{x(1 + x)}}{1})

= (1 + 2x + 2sqrt{x(1 + x)})

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