Question

Rationalise the denominator and simplify : 4√3-
6÷4√3+6​

Answer 1

Answer:

6+436−43=−7+43

Step-by-step explanation:

\frac{6-4\sqrt{3}}{6+4\sqrt{3}}6+436−43

=\frac{6-4\sqrt{3}}{6+4\sqrt{3}}*\frac{6-4\sqrt{3}}{6-4\sqrt{3}}=6+436−43∗6−436−43

=\frac{(6-4\sqrt{3})^2}{(6-4\sqrt{3})(6+4\sqrt{3})}=(6−43)(6+43)(6−43)2

=\frac{36+48-48\sqrt{3}}{36-48}=36−4836+48−483

=\frac{84-48\sqrt{3}}{-12}=−1284−483

=\frac{84}{-12}-\frac{48\sqrt{3}}{-12}=−1284−−12483

=-7+4\sqrt{3}=−7+43

Answer 2

$\frac{(4\sqrt{3}-6)}{(4\sqrt{3}+6)}$

$= \frac{(4\sqrt{3}-6)(4\sqrt{3} -6)}{(4\sqrt{3}+6)(4\sqrt{3} - 6)}$

$= \frac{(4\sqrt{3}-6)^{2}}{(4\sqrt{3})^{2}-6^{2}}$

$= \frac{ (4\sqrt{3})^{2}-2\times 4\sqrt{3} \times 6 + 6^{2} }{48 - 36 }$

$= \frac{ 48 - 48\sqrt{3} + 36 }{12}$

$= \frac{84-48\sqrt{3}}{12}$

$= \frac{12(7 - 4\sqrt{3})}{12}$

$= 7-4\sqrt{3}$

Therefore.,

$\red{\frac{(4\sqrt{3}-6)}{(4\sqrt{3}+6)}}$

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

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