Giải thích các bước giải:
$A=\dfrac{5}{x+xy+1}+\dfrac{5}{y+yz+1}+\dfrac{5}{z+zx+1}$
$\to A=5(\dfrac{1}{x+xy+1}+\dfrac{1}{y+yz+1}+\dfrac{1}{z+zx+1})$
$\to A=5(\dfrac{1}{x+xy+1}+\dfrac{x}{xy+xyz+x}+\dfrac{xy}{xyz+xy.zx+xy})$
$\to A=5(\dfrac{1}{x+xy+1}+\dfrac{x}{xy+1+x}+\dfrac{xy}{1+x+xy})$ vì $xyz=1$
$\to A=5.\dfrac{1+x+xy}{1+x+xy}$
$\to A=5$