Chứng minh đẳng thức: (y-z)/(x-y)(x-z)+(z-x)/(y-z)(y-x)+(x-y)/(z-x)(z-y)=2/(x-y)+2/(y-z)

y−z(x−y)(x−z)+z−x(y−z)(y−x)+x−y(z−x)(z−y)

=(x−z)−(x−y)(x−y)(x−z)+(y−x)−(y−z)(y−z)(y−x)+(z−y)−(z−x)(z−x)(z−y)

=1x−y−1x−z+1y−z−1y−x+1z−x−1z−y

=1x−y+1z−x+1y−z+1x−y+1z−x+1y−z

=2x−y+2y−z+2z−x