Question

Simplify 6-4 ×root 3 /6+4×root 3 by rationalizing the denominateator

Answer 1

(6- 4√3)/ (6+ 4√3)
={(6-4√3)× (6- 4√3)} / {(6+ 4√3)× (6-4√3)}
={(6-4√3)^2} / { 6^2 - (4√3)^2}
= {36 + 48 - 36√3} / {36 - 48}
= (84 -36√3) / (-12)
= -12(3√3 - 7) / (-12)
= (3√3 - 7)

I hope this will help you...

Answer 2

Answer:

The simplification is $\frac{6-4\sqrt3}{6+4\sqrt3}=4\sqrt3-7$    

Step-by-step explanation:

Given : Expression $\frac{6-4\sqrt3}{6+4\sqrt3}$

To find : Simplify the expression by rationalizing the denominator?

Solution :

Expression $\frac{6-4\sqrt3}{6+4\sqrt3}$

Rationalizing the denominator by multiplying and divide by denominator,

$=\frac{6-4\sqrt3}{6+4\sqrt3}\times\frac{6-4\sqrt3}{6-4\sqrt3}$

$=\frac{(6-4\sqrt3)^2}{(6+4\sqrt3)^2}$

$=\frac{36+16\times 3-2\times 6\times4\sqrt3}{6^2-(4\sqrt3)^2}$

$=\frac{36+48-48\sqrt3}{36-48}$

$=\frac{84-48\sqrt3}{-12}$

$=-\frac{12(7-4\sqrt3)}{12}$

$=4\sqrt3-7$

So, The simplification is $\frac{6-4\sqrt3}{6+4\sqrt3}=4\sqrt3-7$