How do you simplify #(3sqrt3)/(-2+sqrt6)#?

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Answer 1 · 2017-07-21T16:09:35

See a solution process below:

The first step is to rationalize the denominator by multiplying the fraction by the appropriate form of #1#:

#(3sqrt(3))/(-2 + sqrt(6)) xx (-2 - sqrt(6))/(-2 - sqrt(6)) =>#

#(3sqrt(3)(-2 - sqrt(6)))/((-2)^2 + (-2 * -sqrt(6)) + (-2 * sqrt(6)) - (sqrt(6))^2) =>#

#((-2 * 3sqrt(3)) - (sqrt(6) * 3sqrt(3)))/(4 + 0 - 6) =>#

#(-6sqrt(3) - 3sqrt(6 * 3))/(-2) =>#

#(-6sqrt(3))/(-2) - (3sqrt(18))/(-2) =>#

#3sqrt(3) + (3sqrt(9 * 2))/2 =>#

#3sqrt(3) + (3sqrt(9)sqrt(2))/2 =>#

#3sqrt(3) + (3 * 3sqrt(2))/2 =>#

#3sqrt(3) + (9sqrt(2))/2#

Answer 2 · 2017-07-21T17:57:26

#3sqrt3+(9sqrt2)/2#

#(3sqrt3)/(-2+sqrt6)#

#:.-(3sqrt3)/(-2+sqrt6) xx (-2-sqrt6)/(-2-sqrt6)#

#:.=(-6sqrt3-9sqrt2)/-2#

#:.=(cancel(-6)^3sqrt3)/cancel(-2)^1-(9sqrt2)/-2#

#:.=3sqrt3-(9sqrt2)/(-2)#

#:.=3sqrt3+((-9sqrt2)/1 xx 1/-2)#

#:.=3sqrt3+(9sqrt2)/2#

~~~~~~~~~~~~~~~~~~~~~~~~

#check#

#:.(3sqrt3)/(-2+sqrt6)=11.56011345#

#:.(-6sqrt3-9sqrt2)/-2=11.56011345#

#:.3sqrt3+(9sqrt2)/2=11.56011345#