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 is A

\(\frac{\sqrt{1 + a} - \sqrt{a}}{1 + a + \sqrt{a}}\) = \(\frac{\sqrt{1 + a} - \sqrt{a}}{\sqrt{1 + a} + \sqrt{a}}\) 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\(\sqrt{a(1 + a)}\)