Вправа 301 - 400 » 359

359. Спрости вираз: a) 1/((a-b)(b- c)) + 1/((c- a)(a- b)) + 1/((b- c)(c- a)) = (c-a + b- c )/((a- b)(b- c)(c- a)) + 1/((b- c)(c- a)) = (b- a)/((a- b)(b- c)(c-a)) + 1/((b- c)(c- a)) = (-1)/((b- c)(c-a)) + 1/((b-c)(c- a)) = 0; б) x^2/((x- y)(x- z)) + y^2/((y - x)(y- z)) + z^2/((z- x)(z- y)) = (x^2 y-x^2 z- xy^2+y^2 z )/((x- y)(x- z)(y- z)) + z^2/((z- x)(z- y)) = (x^2 y- x^2 z- xy^2+y^2 z)/((x- y)(x- z)(y- z)) + z^2/((z- x)(z- y)) = (x^2 y-x^2 z- xy^2+y^2 z+ xz^2- yz^2 )/((x- y)(x- z)(y- z)) = (xy(x- y)- z〖(x〗^2-y^2)+ z^2 (x- y) )/((x- y)(x- z)(y-z)) = (〖(x- y)(xy- zx- zy+ z〗^2))/((x- y)(x- z)(y- z)) = (x(y- z)- z(y- z))/((x- z)(y- z)) = ((y- z)(x- z))/((x- z)(y-z)) = 1.