作业帮数学分式加减题
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 13:19:12
数学分式加减题
数学分式加减题
数学分式加减题
先看x/(xy+x+1),因为xyz=1 ,带入其中的1,可得:
x/(xy+x+1)=1/(y+1+yz)
再看z/(xz+z+1),把分子分母同时乘以y带入可得:
z/(xz+z+1)=zy/(y+1+yz)
这样三者分母相同了,可以合并了,结果为:
x/(xy+x+1) + y/(yz+y+1) + z/(xz+z+1)
=1/(y+1+yz)+y/(yz+y+1)+zy/(y+1+yz)
=1
清楚些的:
x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)
=x/(xy+x+xyz)+y/(yz+y+1)+z/(xz+z+1)
=1/(y+1+yz)+y/(yz+y+1)+z/(xz+z+1)
=(1+y)/(y+1+yz)+z/(xz+z+1)
=(1+y)/(y+1+yz)+zy/(yxz+yz+y)
=(1+y)/(y+1+yz)+zy/(1+yz+y)
=(1+y+yz)/(y+1+yz)
=1
x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)
=x/(xy+x+xyz)+y/(yz+y+1)+z/(xz+z+1)
=1/(y+1+yz)+y/(yz+y+1)+z/(xz+z+1)
=(1+y)/(y+1+yz)+z/(xz+z+1)
=(1+y)/(y+1+yz)+zy/(yxz+yz+y)
=(1+y)/(y+1+yz)+zy/(1+yz+y)
=(1+y+yz)/(y+1+yz)
=1