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a) б) в) г) д) е) ......................................................................................................................................................................

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Erick14 @Erick14

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a) $ab^{-1}+a^{-1}b=\frac{a}{b}+\frac{b}{a}=\frac{a^2+b^2}{ab}$

б) $(ab)^{-1}+(ab)^2=\frac{1}{ab}+a^2b^2=\frac{1+a^3b^3}{ab}$

в) $a^{-1}(a^{-1}-b^{-1})=\frac{1}{a}(\frac{1}{a}-\frac{1}{b})=\frac{1}{a}*\frac{b-a}{ab}=\frac{b-a}{a^2b}$

г) $b^2(a^{-2}-b^{-2})=b^2(\frac{1}{a^2}-\frac{1}{b^2})=b^2*\frac{b^2-a^2}{a^2b^2}=\frac{b^2-a^2}{a^2}$

д) $(a^{-1}+b^{-1})(a+b)^{-1}=(\frac{1}{a}+\frac{1}{b})*\frac{1}{a+b}=\frac{a+b}{ab}*\frac{1}{a+b}=\frac{1}{ab}$

е) $(a^{-1}+b)(a-b^{-1})=(\frac{1}{a}+b)(a-\frac{1}{b})=\frac{1+ab}{a}*\frac{ab-1}{b}=\frac{a^2b^2-1}{ab}$

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