Question

simplify 6-4√3|/6+4√3 by rationalizing the denominator

Answer 1

Answer:

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

Step-by-step explanation:

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

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

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

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

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

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

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

Answer 2

Answer:

-7 + 4√3

Step-by-step explanation:

simplify 6-4√3|/6+4√3 by rationalizing the denominator

(6-4√3)/(6+4√3)

Multiplying numerator & denominator by 6 - 4√3

= (6-4√3)²/((6+4√3)(6-4√3))

Using ( a - b)² = a² + b² - 2ab

(a + b)(a -b) = a² - b²

6² = 36      (4√3)² = 48

= (36 + 48 - 48√3)/(36 - 48)

= (84 - 48√3)/(-12)

= -7 + 4√3