Доказать тождество 7n/98-8n^2:(2n-7/2n+7-2n+7/2n-7)=одна восьмая

Question

Доказать тождество
7n/98-8n^2:(2n-7/2n+7-2n+7/2n-7)=одна восьмая

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Answer 1

1. (2n-7)/(2n+7)-(2n+7)/(2n-7)=((2n-7)²-(2n+7)²)/((2n-7)(2n+7))=
=(4n²-28n+49-(4n²+28n+49))/(4n²-49)=-56n/(4n²-49)=56n/(49-4n²).
2. 7n/(98-8n²):(56n/(49-4n²))=7n*(49-4n²)/(56n*2*(49-4n²))=7n/112n=1/16.