\(=\dfrac{\left(x+y\right)^3+z^3-3xy\left(x+y\right)-3xyz}{\left(x-y\right)^2+\left(y-z\right)^2+\left(x-z\right)^2}\)
\(=\dfrac{\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2\right)-3xy\left(x+y+z\right)}{2\left(x^2+y^2+z^2-xy-xz-yz\right)}\)
\(=\dfrac{\left(x+y+z\right)\left(x^2+y^2+z^2-xy-xz-yz\right)}{2\left(x^2+y^2+z^2-xy-xz-yz\right)}\)
\(=\dfrac{x+y+z}{2}\)
Rút gọn các phân thức: \(\dfrac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+z\right)^2+\left(z-x\right)^2}\)
Rút gọn
\(\dfrac{x^3+y^3+z^3-3xyz}{xy^2+xz\left(2y+z\right)}.\dfrac{x\left(y^2+z\right)+y\left(x-xy\right)}{\left(x-y\right)^2+\left(y-z\right)^2+\left(x-z\right)^2}\)
\(\dfrac{x^3+y^3+z^3-3xyz}{\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2}\)
rút gọn
Rút gọn phân thức:
\(a,\dfrac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+z\right)^2+\left(z-x\right)^2}\)
\(b,\dfrac{\left(x^2-y\right)\left(y+1\right)+x^2y^2-1}{\left(x^2+y\right)\left(y+1\right)+x^2y^2+1}\)
Cho \(x^3+y^3+z^3=3xyz\) .Rút gọn P= \(\dfrac{xyz}{\left(x+y\right)\left(y+z\right)\left(z+x\right)}\)
rút gon:\(B=\dfrac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+z\right)^2+\left(z-x\right)^2}\)
Cho x, y, z đôi một khác nhau thỏa mãn: \(x^3+y^3+z^3=3xyz\) và \(xyz\ne0\). Tính: \(B=\dfrac{16.\left(x+y\right)}{z}+\dfrac{3.\left(y+z\right)}{x}-\dfrac{2019.\left(x+z\right)}{y}\)
Rút gọn biểu thức: B = \(\frac{x^3-y^3-z^3-3xyz}{\left(x+y\right)^2+\left(y-z\right)^2+\left(x+z\right)^2}\)
Rút gọn: \(\dfrac{x^2+y^2+z^2}{\left(y-z\right)^2+\left(z-x\right)^2+\left(x-y\right)^2}\), biết rằng: x+y+z=0
