Question

Simply 6-4 root 3/ 6+4 root 3 by ratnolising the denominator

Answer 1

Answer:

-7+4√3.

Step-by-step explanation:

6-4√3 / 6+4√3     Multiply top and bottom by  6-4√3:-

=  (6-4√3)( 6-4√3) / (6+4√3)(6- 4√3)

= (36-24√3- 24√3+48) / (36-48)

= (36-48√3+48) / (-12)

= -3 +4√3 - 4

=  -7 + 4√3.

Answer 2

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

the question asks us to rationalise the given expression !

so let's start ~

$\frac{6 - 4 \sqrt{3} }{6 + 4 \sqrt{3} } \\ \\ \implies \: \frac{6 - 4 \sqrt{3} }{6 + 4 \sqrt{3} } \: \times \: \frac{6 - 4 \sqrt{3} }{6 - 4 \sqrt{3} } = \frac{(6 - 4 \sqrt{3}) {}^{2} }{6 {}^{2} - 4 \sqrt{3} {}^{2} } \\ \\ \implies \frac{\: 6 {}^{2} + 4 \sqrt{3} {}^{2} - (2 \times 6 \times 4 \sqrt{3} )}{36 - 48} \\ \\ \implies \: \frac{36 + 48 - 48 \sqrt{3} }{ - 12} \\ \\ \implies \: \frac{84 + 48 \sqrt{3} }{ - 12} \\ \\ \implies \: \frac{ \cancel{- 12}(7 - 4 \sqrt{3} )}{ \cancel{ - 12} } \\ \\ \implies \: 7 - 4 \sqrt{3}$

hope helpful :D