向各位高手请教一道数学题

设p/(x²-yz)=q/(y²-zx)=r/(z²巧陆卖-xy)=k，则
p=k(x²-yz)
q=k(y²-zx)
r=k(z²-xy)
三式相加得
p+q+r=k(x²+y²+z²-xy-yz-zx)=9
(px+qy+rz)/悉态(x+y+z)
=(xk(x²-yz)+yk(y²-zx)+zk(z²-xy))/(x+y+z)
=k(x³-xyz+y³-xyz+z³-xyz)/(x+y+z)
=k(x³+y³+z³-3xyz)/(x+y+z)
而x³+y³孝逗+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-zx)
所以(px+qy+rz)/(x+y+z)=k(x²+y²+z²-xy-yz-zx)=9

不会

p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy)=(p+q+r)/(x^2+y^2+z^2-yz-zx-xy) ..........A
p/(x^2-yz)=q/则尺桥(y^2-zx)=r/(z^2-xy)=(px+qy+rz)/(x^3+y^3+z^3-3xyz) ..........B

由A, B可得：孙猛

(p+q+r)/(x^2+y^2+z^2-yz-zx-xy)=(px+qy+rz)/(x^3+y^3+z^3-3xyz)=(px+qy+rz)/(x^2+y^2+z^2-yz-zx-xy)(x+y+z)

=>(px+qy+rz)/困如(x+y+z)=p+q+r=9

我也不知对不敏桥旁。
设：p/(x²-yz)=q/(y²-zx)=r/(z²-xy)=k，则p=k(x²-yz)，q=k(y²-zx)，
r=k(z²-xy)
三式相加得
p+q+r=k(x²+y²+z²-xy-yz-zx)=9
(px+qy+rz)/(x+y+z)=(xk(x²-yz)+yk(y²-zx)+zk(z²-xy))/(x+y+z)=k(x³-xyz+y³-xyz+z³-xyz)/消袜(x+y+z)=k(x³+y³+z³-3xyz)/(x+y+z)

而x³+y³+z³-3xyz=(x+y+z)(x²+y²桥橡+z²-xy-yz-zx)
∴(px+qy+rz)/(x+y+z)=k(x²+y²+z²-xy-yz-zx)=9