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#