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Question Number 191395 by Mingma last updated on 23/Apr/23

Answered by Rasheed.Sindhi last updated on 23/Apr/23

xy+yz+zx=0; ((y+z)/x)+((x+z)/y)+((x+y)/z)=? ((y+z)/x)+((x+z)/y)+((x+y)/z) =((y+z)/x)+1+((x+z)/y)+1+((x+y)/z)+1−3 =((x+y+z)/x)+((x+y+z)/y)+((x+y+z)/z)−3 =(x+y+z)((1/x)+(1/y)+(1/z))−3 =(x+y+z)(((xy+yz+zx)/(xyz)))−3 =(x+y+z)((0/(xyz)))−3=−3

xy+yz+zx=0;y+zx+x+zy+x+yz=?y+zx+x+zy+x+yz=y+zx+1+x+zy+1+x+yz+1−3=x+y+zx+x+y+zy+x+y+zz−3=(x+y+z)(1x+1y+1z)−3=(x+y+z)(xy+yz+zxxyz)−3=(x+y+z)(0xyz)−3=−3

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