化简:(2x-y-z)/(x-y)(x-z)+(2y-z-x)/(y-z)(y-x)+(2z-x-y)/(z-x)(z-y)化简:_数学解答

化简:(2x-y-z)/(x-y)(x-z)+(2y-z-x)/(y-z)(y-x)+(2z-x-y)/(z-x)(z-y)
化简:(2x-y-z)/(x-y)(x-z)+(2y-z-x)/(y-z)(y-x)+(2z-x-y)/(z-x)(z-y)我知道把分母化成一样的、但是之后怎么算?

人气：307 ℃　时间：2020-01-30 10:07:59

解答

令a = x - y,b = y - z,c = z - x原式= (a - c)/(-ac) + (b - a)/(-ba) + (c - b)/(-cb)= (a - b)/ab + (b - c)/bc + (c - a)/ca= [(ac - bc) + (ab - ac) + (bc - ab)]/abc= 0/abc= 0