Question

ДАЮ 80 БАЛЛОВ!!!
Чему равно значение выражения 1/(a-b)*(a-c) - 1/(a-b)*(b-c) + 1/(c-a)*(c-b), если a = 0.7, b = -1.2, c = 4.3

Answer 1

$\displaystyle \frac{1}{(a-b)(a-c)}-\frac{1}{(a-b)(b-c)}+\frac{1}{(c-a)(c-b)}=\\\\=\frac{(b-c)-(a-c)}{(a-b)(a-c)(b-c)}+\frac{1}{(c-a)(c-b)}=\\\\=\frac{b-a}{(a-b)(a-c)(b-c)}+\frac{1}{(c-a)(c-b)}=\frac{-1}{(a-c)(b-c)}+\frac{1}{-(a-c)(c-b)}=\\\\=\frac{-1}{(a-c)(b-c)}+\frac{1}{(a-c)(b-c)} =0$