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Answer: -8 root 5
Step-by-step explanation:
( root 5 - 2 ) / ( root 5 +2 ) - ( root 5 +2 ) / ( root 5 - 2 )
Taking LCM then,
= [ ( root 5 - 2 )^2 - ( root 5 + 2 )^2 ] / [ ( root 5 +2 ) ( root 5 - 2 ) ]
Using formula a^2 -b^2 = (a-b) (a+b)
= ( root 5 - 2 + root 5 + 2 ) ( root 5 - 2 -root 5 -2 ) / [ ( root 5 +2 ) ( root 5 - 2 ) ]
= 2 root 5 * ( -4 ) / ( root 5)^2 - 2^2
= -8 root 5 / ( 5-4)
= -8 root 5
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