How do you rationalize the denominator and simplify #3/(2-sqrt6)#?

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Answer 1 · 2016-06-16T10:42:41

#3/(2-sqrt6)=-3-3/2sqrt6#

To rationalize denominator and simplify #3/(2-sqrt6)#,

one should multiply numerator and denominator of the fraction by conjugate irrational number of denominator #2-sqrt6#, which is #2+sqrt6#.

Hence #3/(2-sqrt6)=3/(2-sqrt6)xx(2+sqrt6)/(2+sqrt6)#

= #(3(2+sqrt6))/((2-sqrt6)(2+sqrt6))#

= #(6+3sqrt6)/(2^2-(sqrt6)^2)#

= #(6+3sqrt6)/(4-6)#

= #(6+3sqrt6)/(-2)#

= #-3-3/2sqrt6#