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Let the fraction = a/b According to the 1st condition; (a/b)+(11/30) = b/a . ....(1) According to the 2nd condition; (a-1)/b = 2/3 => 3a - 3 = 2b =>3a – 2b = 3 .. (2) By solving equation 1, => 30a2+11ab-30b2 = 0 => (6a-5b)(5a+6b)=0 we get the value of a/b = 5/6,-6/5 applying condition(2), a/b = (5-1)/6 = 4/6 = 2/3 Hence the required fraction = a/b = 5/6
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