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Answer»

This problem can be solved by rationalising the terms

(1/2+root 5 x 2 - root 5 /2-root 5) + (1/root 5+root 6 x root 5 -root6/root 5 -root 6) + (1/root6 + root 7 x root 6 -root 7/root 6- root 7) + (1/root7 +root8 x root 7 - root 8 /root 7 - root 8) + (1/root 8 + root9 x root 8 - root 9 /root 8 - root 9) +

= (2 - root 5/ -1 ) + ( root 5 - root 6 / -1) + (root 6 - root 7 / -1 ) + ( root 7 - root 8 / -1 ) + (root 8 - root 9/-1)

= - 2 + root 5 - root 5 + root6 - root 6 + root 7 - root 7 + root 8 - root 8 + root 9

= - 2 + root 9

= - 2 + 3

= 1



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