Question

Решите номер 45.Есть вложение.

Answer 1

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

$(y^{-2}-x^{-2})^{-1}(x^{-1}-y^{-1})= frac{x^{-1}-y^{-1}}{y^{-2}-x^{-2}} = cfrac{ frac{1}{x} - frac{1}{y} }{ frac{1}{y^2}- frac{1}{x^2} } = \ =cfrac{ frac{y-x}{xy} }{ frac{x^2-y^2}{x^2y^2} } = frac{(y-x)x^2y^2}{xy(x^2-y^2)}=frac{(y-x)xy}{(x-y)(x+y)}=-frac{xy}{x+y}$