Simplify: #frac{\sqrt 6 }{\sqrt 2 + \sqrt 3 } + \frac{3\sqrt 2}{\sqrt 6 + \sqrt 3 } - \frac{4\sqrt 3 }{\sqrt 6 + \sqrt 2 }# Please simply this?
2 Answers
See the answer below...
Explanation:
#sqrt6/(sqrt2+sqrt3)+(3sqrt2)/(sqrt6+sqrt3)-(4sqrt3)/(sqrt6+sqrt2)#
#=(sqrt6 cdot (sqrt2-sqrt3))/((sqrt2+sqrt3) cdot (sqrt2-sqrt3))+((3sqrt2)cdot(sqrt6-sqrt3))/((sqrt6+sqrt3)(sqrt6-sqrt3))-(4sqrt3 cdot (sqrt6-sqrt2))/((sqrt6+sqrt2)cdot (sqrt6-sqrt2))#
#=((sqrt12-sqrt18))/(2-3)+((3sqrt12-3sqrt6))/(6-3)-((4sqrt18-4sqrt6))/(6-2)#
#=((sqrt12-sqrt18))/-1+((3sqrt12-3sqrt6))/3-((4sqrt18-4sqrt6))/(4)#
#=(-sqrt12+sqrt18)+(sqrt12-sqrt6)-(sqrt18-sqrt6)#
#=cancel(-sqrt12)+cancel(sqrt18)+cancel(sqrt12)-cancel(sqrt6)-cancel(sqrt18)+cancel(sqrt6)#
#=0# This is the simplied form.
Hope it helps...
Thank you...