Question 685932
{{{2/(4+sqrt(6)) - 2/(4-sqrt(6))}}}


{{{(2(4-sqrt(6)))/((4+sqrt(6))(4-sqrt(6))) - 2/(4-sqrt(6))}}}


{{{(8-2sqrt(6))/((4+sqrt(6))(4-sqrt(6))) - 2/(4-sqrt(6))}}}


{{{(8-2sqrt(6))/((4+sqrt(6))(4-sqrt(6))) - (2(4+sqrt(6)))/((4+sqrt(6))(4-sqrt(6)))}}}


{{{(8-2sqrt(6))/((4+sqrt(6))(4-sqrt(6))) - (8+2sqrt(6))/((4+sqrt(6))(4-sqrt(6)))}}}


{{{(8-2sqrt(6) - (8+2sqrt(6)))/((4+sqrt(6))(4-sqrt(6)))}}}


{{{(8-2sqrt(6) - 8 - 2sqrt(6))/((4+sqrt(6))(4-sqrt(6)))}}}


{{{(-4sqrt(6))/((4+sqrt(6))(4-sqrt(6)))}}}


{{{(-4sqrt(6))/((4)^2- (sqrt(6))^2)}}}


{{{(-4sqrt(6))/(16 - 6)}}}


{{{(-4sqrt(6))/(10)}}}


{{{(-2sqrt(6))/(5)}}}


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Answer:


So {{{2/(4+sqrt(6)) - 2/(4-sqrt(6)) = (-2*sqrt(6))/(5)}}}