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Simplify \(\frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 + x} - \sq...

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 is B

\(\frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 + x} - \sqrt{x}}\)

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

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

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

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