How do you simplify $-20/(sqrt6 - sqrt2)$ ?

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Answer 1 · 2016-02-24T03:19:55

Rationalize the denominator to find that

$-20/(sqrt(6)-sqrt(2))=-5(sqrt(6)+sqrt(2))$

We will use the fact that $(a-b)(a+b) = a^2-b^2$ to rationalize the denominator.

$-20/(sqrt(6)-sqrt(2)) = -(20(sqrt(6)+sqrt(2)))/((sqrt(6)-sqrt(2))(sqrt(6)+sqrt(2))$

$=-(20(sqrt(6)+sqrt(2)))/((sqrt(6))^2-(sqrt(2))^2)$

$=-(20(sqrt(6)+sqrt(2)))/(6-2)$

$=-(20(sqrt(6)+sqrt(2)))/4$

$=-5(sqrt(6)+sqrt(2))$

How do you simplify -20/(sqrt6 - sqrt2)-20/(sqrt6 - sqrt2)?