Simplify \( \frac{6}{2\sqrt 3 - 3}\) as much as possible.
Thanks! Please explain.
6/(2 sqrt(3) - 3) -Simplify:
Multiply numerator and denominator of 6/(2 sqrt(3) - 3) by 2 sqrt(3) + 3:
(6 (2 sqrt(3) + 3))/((2 sqrt(3) - 3) (2 sqrt(3) + 3))
(2 sqrt(3) - 3) (2 sqrt(3) + 3) = -3×3 - 3×2 sqrt(3) + 2 sqrt(3)×3 + 2 sqrt(3)×2 sqrt(3) = -9 - 6 sqrt(3) + 6 sqrt(3) + 12 = 3:
(6 (2 sqrt(3) + 3))/3
6/3 = (3×2)/3 = 2:
=2 (2 sqrt(3) + 3)
6/(2 sqrt(3) - 3) -Simplify:
Multiply numerator and denominator of 6/(2 sqrt(3) - 3) by 2 sqrt(3) + 3:
(6 (2 sqrt(3) + 3))/((2 sqrt(3) - 3) (2 sqrt(3) + 3))
(2 sqrt(3) - 3) (2 sqrt(3) + 3) = -3×3 - 3×2 sqrt(3) + 2 sqrt(3)×3 + 2 sqrt(3)×2 sqrt(3) = -9 - 6 sqrt(3) + 6 sqrt(3) + 12 = 3:
(6 (2 sqrt(3) + 3))/3
6/3 = (3×2)/3 = 2:
=2 (2 sqrt(3) + 3)
