设函数y=2/x与y=x-1的图像的交点坐标为(a,b),则1/a-1/b的值为多少

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设函数y=2/x与y=x-1的图像的交点坐标为(a,b),则1/a-1/b的值为多少

y = 2/x
y = x - 1
解此方程组得:
x = -1时,y = -2 或 x = 2,y = 1
所以 a = -1,b = -2 或 a = 2 ,b = 1
当 a = -1,b = -2 时,1/a - 1/b = 1/(-1) - 1/(-2) = -1/2
当 a = 2,b = 1 时,1/a - 1/b = 1/2 - 1/1 = -1/2
综上:1/a - 1/b = -1/2

y = 2/x
y = x - 1
解此方程组得:
x = -1时,y = -2 或 x = 2,y = 1
所以 a = -1,b = -2 或 a = 2 ,b = 1
当 a = -1,b = -2 时,1/a - 1/b = 1/(-1) - 1/(-2) = -1/2
当 a = 2,b = 1 时,1/a - 1/b = 1/2 - 1/1 = -1/2
综上:1/a - 1/b = -1/2

若相交,则有2/x=x-1,解得:x=2或x=-1,当x=2时,y=1,则(a,b)就是(2,1),
所以1/a-1/b=-1/2
当x=-1时,y=-2,则(a,b)就是(-1,-2),
所以1/a-1/b=-1/2

b=2/a, b=a-1
ab=2, b-a=-1
1/a-1/b=(b-a)/ab=-1/2