Rationalize rac{{2} + {3}}{{2} - {3}}

Correct Answer is : −5−26-5 - 2{6}−5−26

Correct Answer is : −5−26-5 - 2{6}−5−26

Test Index

JAMB Mathematics 2019 Paper

Question : 6

Total: 73

Rationalize

rac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}

Solution:

Concept:

Rationalize a fraction with a surd denominator by multiplying the numerator and denominator by the conjugate of the denominator.

Explanation:

Given expression:

\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}

The conjugate of

\sqrt{2} - \sqrt{3}

\sqrt{2} + \sqrt{3}

Multiply the numerator and denominator by the conjugate:

\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}} \times \frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}}

Expand the numerator:

(\sqrt{2} + \sqrt{3})^{2} = 2 + 2\sqrt{6} + 3 = 5 + 2\sqrt{6}

Expand the denominator using difference of two squares:

(\sqrt{2})^{2} - (\sqrt{3})^{2} = 2 - 3 = -1

Therefore:

\frac{5 + 2\sqrt{6}}{-1} = -5 - 2\sqrt{6}

Answer:

-5 - 2\sqrt{6}

(Option A).

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