Question

Rationalising the denominator
6-4√3
———
6+4√3

Answer 1

6-4√3/6+4√3 ×6-4√3/6-4√3
(6-4√3)²/(6)²-(4√3)²
36+48-48√3 / 36-48
84-48√3/ -14
2(42-24√3)/ 2(-7)
42-24√3/-7
-42+24√3/7
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Answer 2

Here your answer:
$(6 - 4 \sqrt{3}) \: \: \: \: \: \: \: (6 - 4 \sqrt{3} ) \\ - - - - \times - - - - - \\ (6 + 4 \sqrt{3}) \: \: \: \: \: \: (6 - 4 \sqrt{3})$
${6}^{2} + ({4 \sqrt{3}) }^{2} - 2 \times 6 \times 4 \sqrt{3} \\ - - - - - - - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {6}^{2} - ( {4 \sqrt{3})}^{2}$
$36 + 16 \times 3 - 48 \sqrt{3} \\ - - - - - - - - - - \\ \: \: \: \: \: \: 36 - (16 \times 3)$
$36 + 48 - 48 \sqrt{3} \\ - - - - - - - - \\ \: \: \: \: \: \: \: \: \: 36 - 48$
$84 - 48 \sqrt{3} \\ - - - - - - \\ \: \: \: \: \: \: ( - 12)$
$- 84 + 48 \sqrt{3} \\ - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: 12$

$48 \sqrt{3} - 84 \\ - - - - - - \\ \: \: \: \: \: \: \: \: \: 12$

FOR SIMPLIEST FORM OF ANSWER:-NOW JUST DIVIDE 48 BY 12 AND 84 BY 12. AND YOU WILL GET:
(4×UNDEROOT3)-7

HOPE IT HELPS YOU!