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)})