Вправи 401 - 467 » 413

413. Знайдіть x/y, якщо: 1) (x^(-1)+y^(-1) )/(x^(-1)- y^(-1) ) = 2; (1/x+ 1/y)/(1/x- 1/y) = 2; ((y+x)/xy)/((y-x)/xy) = 2; ((y+x)•xy)/(xy(y-x)) = 2; (y+x)/(y-x) = 2. 2(y – x) = y + x; 2y – 2x = y + x; –2x – x = y – 2y; –3x = –y|: (–3y); x/y = 1/3; 2) (〖2x〗^(-1)- y^(-1))/(x^(-1)+ 〖2y〗^(-1) ) = 5; (2/x- 1/y)/(1/x+ 2/y) = 5; ((2y-x)/xy)/((y+2x)/xy) = 5; ((2y-x)•xy)/(xy •(y+2x)) = 5; (2y-x)/(y+2x) = 5. 5(y + 2x) = 2y – x; 5y + 10x = 2y – x; 10x + x = 2y – 5y; 11x = –3y| : 11y; x/y = –3/11.