JAMB 1991 · UME · Q24

Simplify $\dfrac{\sqrt{1 + x} + \sqrt x}{\sqrt{1 + x} - \sqrt x}$ .

Worked solution (try it first)

Multiply the top and bottom by the conjugate of the bottom, $\sqrt{1 + x} + \sqrt x$ .
Bottom: $(\sqrt{1 + x})^2 - (\sqrt x)^2 = (1 + x) - x$ , which is 1.
Top: $(\sqrt{1 + x} + \sqrt x)^2 = (1 + x) + 2\sqrt{x(1 + x)} + x$ , which is $1 + 2x + 2\sqrt{x(1 + x)}$ .
So option B.