Đáp án:
$\dfrac{a}{ab + a + 1} +\dfrac{b}{bc + b + 1} +\dfrac{c}{ca + c +1} = 1\Leftrightarrow abc =1$
Giải thích các bước giải:
$\dfrac{a}{ab + a + 1} +\dfrac{b}{bc + b + 1} +\dfrac{c}{ca + c +1}$
$=\dfrac{ac}{abc + ac + c} +\dfrac{abc}{abc^2 + abc + ac} +\dfrac{c}{ca + c +1}$
$= \dfrac{ac}{1 + ac + c} +\dfrac{1}{c + 1+ ac} +\dfrac{c}{ca + c +1}$
$=\dfrac{ac + 1 + c}{ac + 1 + c}$
$=1$
