How do you simplify $-6/(5-sqrt11)$ ?

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Answer 1 · 2017-03-22T21:08:34

$-(30 + 6sqrt(11))/36$

rationalise the denominator.

use this law:
$(a+b)(a-b) = a^2 - b^2$

to rationalise $5-sqrt(11)$ , multiply it by $5+sqrt(11)$ :

$5+sqrt(11)*5-sqrt(11) = 5^2 + (sqrt(11))^2$

$=25+11$

$=36$

multiply the numerator by $5+sqrt(11)$ as well:

$6*(5+ sqrt(11)) = 30 + 6sqrt(11)$

fraction: $-(30 + 6sqrt(11))/36$

How do you simplify -6/(5-sqrt11)-6/(5-sqrt11)?