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Question

Represent the following mixed infinite decimal periodic fractions as common fractions:
Simplify the following expressions.
a+ba2/3a1/3b1/3+b2/3aba2/3+a1/3b1/3b2/3a2/3b2/3a1/3b1/3

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Solution

This question is wrong
Correct question is,
a+ba2/3a1/3.b1/3+b2/3aba2/3+a1/3.b1/3+b2/3a2/3b2/3a1/3b1/3
here put a1/3=x, and b1/3=y
then, we get,
x3+y3x2xy+y2x3y3x2+xy+y2x2y2xy
=(x+y)(x2xy+y2)(x2xy+y2)(xy)(x2+xy+y2)x2+xy+y2(xy)(x+y)(xy)
=(x+y)(xy)(x+y)
=x+yx+yxy
=(xy)
=yx
=b1/3a1/3

1170660_884768_ans_c3743db3be0c496995027384a4cc10f4.jpg

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