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Simplify  \( \frac{6}{2\sqrt 3 - 3}\) as much as possible.

 

Thanks! Please explain.

 Jun 29, 2018

Best Answer 

 #1
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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)

 Jun 29, 2018
 #1
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+1
Best Answer

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)

Guest Jun 29, 2018

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