Rationalize the denominator of the given expression (frac{sqrt{1 + a} – sqrt{a}}{1 + a + sqrt{a}})
-
A.
1 + 2a – 2(sqrt{a(1 + a)}) -
B.
(sqrt{1(1 + a)}) -
C.
2a – 2(sqrt{a(1 + a)}) -
D.
1 + 2a – 2(sqrt{a + b})
Correct Answer: Option A
Explanation
(frac{sqrt{1 + a} – sqrt{a}}{1 + a + sqrt{a}}) = (frac{sqrt{1 + a} – sqrt{a}}{sqrt{1 + a} + sqrt{a}}) x (frac{sqrt{1 + a} – sqrt{a}}{sqrt{1 + a} – sqrt{a}})
= (frac{sqrt{1 + a + a}}{1 + a – a})
= 2a + a(1 + a)
= 1 + 2a – 2(sqrt{a(1 + a)})