JAMB - Mathematics (1981 - No. 20)
Simplify \(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) - \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\)
2\(\sqrt{2} - \sqrt{3}\)
3(\(\sqrt{6}\) - 1)
\(\sqrt{6}\) - 3
-\(\frac{1}{2}\)
\(\frac{-\sqrt{3}}{\sqrt{2} - \sqrt{2}}\)
Explanation
\(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) - \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\)
\(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) = \(\frac{\sqrt{2}}{\sqrt{3}}\) - \(\frac{\sqrt{3}}{\sqrt{2}}\)
\(\frac{\sqrt{3} + \sqrt{2}}{3 + \sqrt{2}}\) = \(\sqrt{6}\) + 2
\(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\) = \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\) x \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}\)
= 5 - 2\(\sqrt{6}\)
\(\sqrt{6}\) + 2 - (5 - 2 \(\sqrt{6}\)) = \(\sqrt{6}\) + 2 - 5 + 2\(\sqrt{6}\)
= 3\(\sqrt{6}\) - 3
= 3(\(\sqrt{6}\) - 1)
\(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) = \(\frac{\sqrt{2}}{\sqrt{3}}\) - \(\frac{\sqrt{3}}{\sqrt{2}}\)
\(\frac{\sqrt{3} + \sqrt{2}}{3 + \sqrt{2}}\) = \(\sqrt{6}\) + 2
\(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\) = \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\) x \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}\)
= 5 - 2\(\sqrt{6}\)
\(\sqrt{6}\) + 2 - (5 - 2 \(\sqrt{6}\)) = \(\sqrt{6}\) + 2 - 5 + 2\(\sqrt{6}\)
= 3\(\sqrt{6}\) - 3
= 3(\(\sqrt{6}\) - 1)
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