数学分式加减题
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数学分式加减题
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![数学分式加减题](/uploads/image/z/16532172-36-2.jpg?t=%E6%95%B0%E5%AD%A6%E5%88%86%E5%BC%8F%E5%8A%A0%E5%87%8F%E9%A2%98)
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)=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