How do you rationalize the denominator $\frac{4 \sqrt{3} + 2}{2 \sqrt{3} + 1}$ $(4sqrt3+2)/(2sqrt3+1)$ ?

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Answer 1 · 2015-06-07T04:10:36

By rationalizing the denominator.

$\frac{2 (2 \sqrt{3} + 1)}{2 \sqrt{3} + 1} . \frac{2 \sqrt{3} - 1}{2 \sqrt{3} - 1}$ $(2(2sqrt3 + 1))/(2sqrt3 + 1).(2sqrt3 - 1)/(2sqrt3 - 1)$ =

$= \frac{2 (12 - 1)}{12 - 1} =$ $= (2(12 - 1))/(12 - 1) =$ 2

By simplification:

$\frac{2 (2 \sqrt{3} + 1)}{2 \sqrt{3} + 1} = 2$ $(2(2sqrt3 + 1))/(2sqrt3 + 1) = 2$

How do you rationalize the denominator 4√3+22√3+1(4sqrt3+2)/(2sqrt3+1)?