# "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 }. #