Cho abc=2020. Rút gọn A= $\frac{2020a}{ab+2020a+2020}$ + $\frac{b}{bc+b+2020}$ + $\frac{c}{ac+c+1}$

Giải thích các bước giải:

Ta có :

$A=\dfrac{2020a}{ab+2020a+2020}+\dfrac{b}{bc+b+2020}+\dfrac{c}{ac+c+1}$

$\to A=\dfrac{2020a}{ab+2020a+2020}+\dfrac{ab}{abc+ab+2020a}+\dfrac{abc}{ab.ac+abc+ab}$

$\to A=\dfrac{2020a}{ab+2020a+2020}+\dfrac{ab}{2020+ab+2020a}+\dfrac{2020}{2020a+2020+ab},abc=2020$

$\to A=\dfrac{2020a+ab+2020}{2020a+2020+ab}$

$\to A=1$