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

Mathematics
JAMB 1991

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\(\sqrt{x (1 + x)}\)
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Correct Answer: Option B
Explanation

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

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

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

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

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


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Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
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