Question

докажите тождество...

Answer 1

$displaystyle frac{abc-a^3}{a^2b}+frac{abc-b^3}{b^2c}+frac{abc-c^3}{c^2a}= \ \ frac{a(bc-a^2)}{a^2b}+ frac{b(ac-b^2)}{b^2c}+frac{c(ab-c^2)}{c^2a}= \ \ frac{bc-a^2}{ab}+frac{ac-b^2}{bc}+frac{ab-c^2}{ac}= \ \ frac{c(bc-a^2)+a(ac-b^2)+b(ab-c^2)}{abc} = \ \ frac{bc^2-a^2c+a^2c-ab^2+ab^2-bc^2}{abc} = frac{0}{abc}=0$