# 9. Simplify by rationalising the denominator: 2+√3 2−√3 + 2−√3 2+√3 .

Question

9. Simplify by rationalising the denominator: 2+√3 2−√3 + 2−√3 2+√3 .

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1 year 2021-09-01T12:03:01+00:00 1 Answers 2 views 0

## Answers ( )

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$$\frac{2 + \sqrt{3} }{2 – \sqrt{3} } + \frac{2 – \sqrt{3} }{2 + \sqrt{3} }$$

$$\\= \frac{2 + \sqrt{3} }{2 – \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } + \frac{2 – \sqrt{3} }{2 + \sqrt{3} } \times \frac{2 – \sqrt{3} }{2 – \sqrt{3} }$$

$$\\= \frac{2 \: (2 + \sqrt{3} )+ \sqrt{3} \: (2 + \sqrt{3} )}{ ({2})^{2} – ({ \sqrt{3} })^{2} } + \frac{2 \: (2 – \sqrt{3} ) – \sqrt{3} \: (2 – \sqrt{3} ) }{ ({2})^{2} – ( { \sqrt{3} })^{2} }$$

$$\\ = \frac{4 + 2 \sqrt{3} + 2 \sqrt{3} + 3 }{4 – 3} + \frac{4 – 2 \sqrt{3} – 2 \sqrt{3} + 3}{4 – 3}$$

$$\\ = \frac{7 + 4 \sqrt{3} }{1} + \frac{7 – 4 \sqrt{3} }{1}$$

$$\\= 7 + 4 \sqrt{3} + (7 – 4 \sqrt{3} )$$

$$\\= 7 + 4 \sqrt{3} + 7 -4 \sqrt{3}$$

$$\\= 14$$

### Note:

$$(a + b)(a – b) = {a}^{2} – {b}^{2}$$

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