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
P dilip_k
Feb 10, 2018

# sqrt 6 /(sqrt 2 + sqrt 3) +(3\sqrt 2)/(sqrt 6 + sqrt 3 ) - (4sqrt 3)/ (sqrt 6 + sqrt 2)#

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

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

# =(sqrt 6 (sqrt 3 - sqrt 2))/1 +(3sqrt 2(sqrt 6 - sqrt 3 ))/3 - (4sqrt 3 (sqrt 6 -sqrt 2))/4#

# =sqrt 6 (sqrt 3 - sqrt 2) +sqrt 2(sqrt 6 - sqrt 3 ) - sqrt 3 (sqrt 6 -sqrt 2)#

# =sqrt 18 - sqrt 12 +sqrt 12 - sqrt 6 - sqrt 18 +sqrt 6=0#

Sunayan S
Feb 10, 2018

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...

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