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

Simplify 1+x+x1+xx

A.

-2x - 2x(1+x)

B.

1 + 2x + 2x(1+x)

C.

x(1+x)

D.

1 + 2x - 2x(1+x)

Correct answer is B

1+x+x1+xx

= (1+x+x1+xx)(1+x+x1+x+x)

= (1+x)+x(1+x)+x(1+x)+x(1+x)x

= 1+2x+2x(1+x)1

= 1+2x+2x(1+x)