How do you simplify #(2sqrt2- 2sqrt3 )/(4sqrt3+4sqrt2)#?

2 Answers
Mar 7, 2018

Answer:

# "The answer is:" \qquad \qquad \qquad \quad { 2 sqrt{2} - 2 sqrt{3} }/{ 4 sqrt{3} - 4 sqrt{2} } \ = \ - { 1 }/{ 2 }. #

Explanation:

# "This one goes quite nicely, thankfully. A minor adjustment of" #
# "the given can add a bit of computational complexity. Anyway," #
# "here we go:" #

# \qquad \qquad \qquad { 2 sqrt{2} - 2 sqrt{3} }/{ 4 sqrt{3} - 4 sqrt{2} } \ = \ { 2 ( sqrt{2} - sqrt{3} ) }/{ 4 ( sqrt{3} - sqrt{2} ) } #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad = \ { 2 (-1)( sqrt{3} - sqrt{2} ) }/{ 4 ( sqrt{3} - sqrt{2} ) } #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad = \ { 2 (-1) color{red}cancel{ ( sqrt{3} - sqrt{2} ) } }/{ 4 color{red}cancel{ ( sqrt{3} - sqrt{2} ) } } #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad = \ { 2 (-1) }/{ 4 } #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad = \ - { 1 }/{ 2 }. #

# "This is our answer !!" #

# "So, we have found:" #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad { 2 sqrt{2} - 2 sqrt{3} }/{ 4 sqrt{3} - 4 sqrt{2} } \ = \ - { 1 }/{ 2 }. #

Mar 7, 2018

Answer:

#1/2 (2sqrt6-5)#

Explanation:

Given, #[2 sqrt2 - 2 sqrt3]/[4 sqrt3 +4 sqrt2]#
#rArr [2(sqrt 2-sqrt 3)]/[4(sqrt3+sqrt2)]#
#rArr 1/2 (sqrt2-sqrt3)/(sqrt3+sqrt2)#
#rArr 1/2 [(sqrt2-sqrt3)(sqrt2-sqrt3)]/[(sqrt3+sqrt2)(sqrt2-sqrt3)]#
#rArr 1/2[(sqrt2)^2-2.sqrt2.sqrt3+(sqrt3)^2]/[2-3+sqrt6-sqrt6]#
#rArr 1/2 [5-2sqrt6]/(-1)#
#rArr 1/2(2sqrt6-5)#