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Question

Represent the following mixed infinite decimal periodic fractions as common fractions:
(a212a)2(a1a+1a+1a1)

Solution
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(a212a)2(a1a+1a+1a1)
=(a12a)2[(a1)2(a+1)2a1]
=(a1)24a4a(a1)
=(a+1)

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