1-a-b/a+2b÷a²-b²/a²+4ab+4b²

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1-a-b/a+2b÷a²-b²/a²+4ab+4b²

=1-(a-b)/(a+2b)×(a+2b)/(a+b)(a-b)
=1-(a+2b)/(a+b)
=[(a+b)-(a+2b)]/(a+b)
=-b/(a+b)