Вправа 201 - 300 » 201

201. Виконай дії: а) 1/(x^2+ 3xy) + 2/(9y^2- x^2 ) + 1/(2x-6y) = 1^(\6y-2x)/(x(x+3y)) + 2^(\2x)/((3y-x)(3y+x)) + 1^(\\-x(3y+x))/(2(x-3y)) = (3y-2x+4x-x(3y+x))/(2x(3y-x)(3y+x)) = (6y+2x-3xy- x^2)/(2x(3y-x)(3y+x)) = (2(3y+x)- x(3y+x))/(2x(3y-x)(3y+x)) = ((3y+x)(2-x))/(2x(3y-x)(3y+x)) = (2-x)/2x(3y-x) ; б) (7- x^2)/(x^3- 1) + (3x+5)/(x^2+ x+1) + 2/(1-x) = (7- x^2)/((x-1)(x^2+ x+1)) + (3x+5)/(x^2+ x+1) + 2/(1-x) = (7- x^2+ (x-1)(3x+5)- 2(x^2+ x+1))/((x-1)(x^2+ x+1)) = (7- x^2+ 〖3x〗^2+ 5x-3x-5-2x^2- 2x-2)/((x-1)(x^2+ x+1)) = 0.