Question

Thực hiện phép tính
\(\dfrac{1}{\left(x-y\right)\left(y-z\right)}+\dfrac{1}{\left(y-z\right)\left(z-x\right)}+\dfrac{1}{\left(z-x\right)\left(x-y\right)}\)

Answer 1

ĐKXĐ: \(x\ne y\ne z\)

\(\dfrac{1}{\left(x-y\right)\left(y-z\right)}+\dfrac{1}{\left(y-z\right)\left(z-x\right)}+\dfrac{1}{\left(z-x\right)\left(x-y\right)}\\ =\dfrac{z-x}{\left(x-y\right)\left(y-z\right)\left(z-x\right)}+\dfrac{x-y}{\left(x-y\right)\left(y-z\right)\left(z-x\right)}+\dfrac{y-z}{\left(x-y\right)\left(y-z\right)\left(z-x\right)}\\ =\dfrac{z-x+x-y+y-z}{\left(x-y\right)\left(y-z\right)\left(z-x\right)}=0\)