Question

已知:1/x-1/y-1/(x+y)=0,求x/y+y/x的值

急~

Answer 1

由1/x-1/y-1/(x+y)=0通分知
y(x+y)-x(x+y)-xy=0 即y*y-x*x-xy=0
上下同除x*x知 （y/x）*(y/x)-(y/x)-1=0
设y/x=t 则t*t-t-1=0 解出t后求t+1/t的值即可

Answer 2

通分后：y(x+y)+x(x+y)-xy=0
y(x+y)+x(x+y)=xy
y(x+y)/xy+x(x+y)/xy=1
(x+y)/x+(x+y)/y=1
1+y/x+x/y+1=1
y/x+x/y=-1