Question

Помогите решить 22 д

Answer 1

$frac{a^{-2}+b^{-2}}{a^{-1}+b^{-1}}cdot( frac{a^2+b^2}{ab})^{-1}-(a+b)^{-1}= frac{ (frac{1}{a})^2 +( frac{1}{b})^2}{ frac{1}{a}+ frac{1}{b}}cdot frac{ab}{a^2+b^2}- frac{1}{a+b}=\\ = frac{ frac{a^2+b^2}{a^2b^2}}{ frac{a+b}{ab}}cdot frac{ab}{a^2+b^2}- frac{1}{ab}= frac{a^2+b^2}{a^2b^2}cdot frac{ab}{a+b}cdot frac{ab}{a^2+b^2} - frac{1}{a+b}= \\ = frac{1}{a+b}- frac{1}{a+b}=0$