分式的题目1已知p/x^2-yz=q/y^2-zx=r/z^2-xy,求证（px+qy+rz）=（x+y+z）*（p+q+r）

Question

分式的题目1
已知 p/x^2-yz = q/y^2-zx = r/z^2-xy ,求证（px+qy+rz）=（x+y+z）*（p+q+r）

Answer 1

设p/x^2-yz = q/y^2-zx = r/z^2-xy =kp=(x^2-yz)k, q=(y^2-zx)k, r=(z^2-xy)kp+q+r=(x^2+y^2+z^2-xy-yz-zx)kpx+qy+rz=(x^2-yz)kx+(y^2-zx)ky+(z^2-xy)kz=k(x^3+y^3+z^3-3xyz)=k(x+y+z)(x^2+y^2+z^2-xy-yz-zx)=(x+y+z...