Question

1.7.15; 1.7.16 пожалуйста

Answer 1

$1)quad frac{(x^2-y^2)^2}{x^2+2xy+y^2}:left (frac{1}{x^2}-frac{1}{y^2}right)= frac{(x^2-y^2)^2}{(x+y)^2}:frac{y^2-x^2}{x^2y^2}=\\=frac{(x^2-y^2)^2}{(x+y)^2}cdot frac{x^2y^2}{-(x^2-y^2)}=-frac{x^2y^2(x^2-y^2)}{(x+y)^2}=-frac{x^2y^2(x-y)(x+y)}{(x+y)^2}=\\=-frac{x^2y^2(x-y)}{x+y}$

$2)quad (frac{1}{a}+frac{1}{b})cdot left ((a+b)^2-frac{a^3-b^3}{a-b}right )=\\=frac{b+a}{ab}cdot left((a+b)^2-frac{(a-b)(a^2+ab+b^2)}{a-b}right )=\\=frac{a+b}{ab}cdot ((a+b)^2-(a^2+ab+b^2))=\\=frac{a+b}{ab}cdot (a^2+b^2+2ab-a^2-ab-b^2)=frac{a+b}{ab}cdot ab=a+b$