Question

Rationalize the denominator and Evaluate

6 − 4√3
/ 6 + 4√3​

Answer 1

Answer:

\frac{6-4\sqrt{3}}{6+4\sqrt{3}}=-7+4\sqrt{3}

6+4

3

6−4

3

=−7+4

3

Step-by-step explanation:

\frac{6-4\sqrt{3}}{6+4\sqrt{3}}

6+4

3

6−4

3

=\frac{6-4\sqrt{3}}{6+4\sqrt{3}}*\frac{6-4\sqrt{3}}{6-4\sqrt{3}}=

6+4

3

6−4

3

∗

6−4

3

6−4

3

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

(6−4

3

)(6+4

3

)

(6−4

3

)

2

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

36−48

36+48−48

3

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

−12

84−48

3

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

−12

84

−

−12

48

3

=-7+4\sqrt{3}=−7+4

3