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

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

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

$$ VT = \left(\frac{1}{a-b} + \frac{1}{c-a}\right) + \left(\frac{1}{b-c} + \frac{1}{a-b}\right) + \left(\frac{1}{c-a} + \frac{1}{b-c}\right) $$

$$ VT = 2\left(\frac{1}{a-b} + \frac{1}{b-c} + \frac{1}{c-a}\right) $$

$$ 2Q = 2024 $$

Suy ra:

$$ Q = \frac{2024}{2} $$

$$ Q = 1012 $$

Vậy, giá trị của biểu thức Q là 1012.