Bạn đã ib nhờ mik thì mik làm cho trót vại UwU
\(\frac{1}{x\left(x-y\right)\left(x-z\right)}+\frac{1}{y\left(y-z\right)\left(y-x\right)}+\frac{1}{z\left(z-x\right)\left(z-y\right)}.\)
\(=-\frac{1}{x\left(x-y\right)\left(z-x\right)}-\frac{1}{y\left(y-z\right)\left(x-y\right)}-\frac{1}{z\left(z-x\right)\left(y-z\right)}\)
\(=-\frac{y^2x-yz^2}{xyz\left(x-y\right)\left(z-x\right)\left(y-z\right)}-\frac{xz^2-x^2z}{xyz\left(x-y\right)\left(z-x\right)\left(y-z\right)}-\frac{x^2y-xy^2}{xyz\left(x-y\right)\left(z-x\right)\left(y-z\right)}\)
\(=\frac{-y^2z+yz^2-xz^2+x^2z-x^2y+xy^2}{xyz\left(x-y\right)\left(z-x\right)\left(y-z\right)}\)
\(=\frac{-\left(y^2z-x^2z\right)+\left(yz^2-xz^2\right)-\left(x^2y-xy^2\right)}{xyz\left(x-y\right)\left(z-x\right)\left(y-z\right)}\)
\(=\frac{-z\left(y^2-x^2\right)+z^2\left(y-x\right)-xy\left(x-y\right)}{xyz\left(x-y\right)\left(z-x\right)\left(y-z\right)}\)
\(=\frac{-z\left(y-x\right)\left(x+y\right)+z^2\left(y-x\right)+xy\left(y-x\right)}{xyz\left(x-y\right)\left(z-x\right)\left(y-z\right)}\)
\(=\frac{\left(y-x\right)\left[-z\left(x+y\right)+x^2+xy\right]}{xyz\left(x-y\right)\left(z-x\right)\left(y-z\right)}\)
\(=\frac{\left(y-x\right)\left[-z\left(x+y\right)+x^2+xy\right]}{-xyz\left(y-x\right)\left(z-x\right)\left(y-z\right)}\)
\(=-\frac{-z\left(x+y\right)+z^2+xy}{xyz\left(z-x\right)\left(y-z\right)}\)
\(=-\frac{-zx-zy+z^2+xy}{xyz\left(z-x\right)\left(y-z\right)}\)
\(=\frac{-\left(zx-xy\right)-\left(zy-z^2\right)}{xyz\left(z-x\right)\left(y-z\right)}\)
\(=\frac{-x\left(z-y\right)-z\left(y-z\right)}{xyz\left(z-x\right)\left(y-z\right)}\)
\(=\frac{x\left(y-z\right)-z\left(y-z\right)}{xyz\left(z-x\right)\left(y-z\right)}\)
\(=\frac{\left(y-z\right)\left(x-z\right)}{xyz\left(z-x\right)\left(y-z\right)}\)
\(=\frac{x-z}{xyz\left(z-x\right)}\)
\(=\frac{-\left(z-x\right)}{xyz\left(z-x\right)}\)
\(=\frac{-1}{xyz}\)
