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

Question

Avery Alexander · Accepted Answer

#-(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#

Julia Adams · Answer

undefined To simplify the expression -6/(5-sqrt11), you can multiply both the numerator and denominator by the conjugate of the denominator, which is 5+sqrt11. This will eliminate the square root in the denominator. Simplifying further, the expression becomes -6(5+sqrt11)/((5-sqrt11)(5+sqrt11)). Expanding the denominator using the difference of squares, the expression simplifies to -6(5+sqrt11)/(25-11). Continuing to simplify, it becomes -6(5+sqrt11)/14. Finally, dividing both the numerator and denominator by 2, the simplified expression is -3(5+sqrt11)/7.