解方程:(1)2/x=3/x+3 (2)x/x-1+1/x=1
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解方程:(1)2/x=3/x+3 (2)x/x-1+1/x=1
(3)已知x^2+x-1=0,求x(1-2/1-x)除(x+1)-x(x^2-1)/x^2-2x+1
(3)已知x^2+x-1=0,求x(1-2/1-x)除(x+1)-x(x^2-1)/x^2-2x+1
(1)
3x=2(x+3)
3x=2x+6
∴x=6
检验:x=6是方程的解
(2) x²+x-1=x(x-1)
x²+x-1=x²-x
2x=1
x=1/2
(3)∵x^2+x-1=0
∴x²=1-x
x(1-2/1-x)除(x+1)-x(x^2-1)/x^2-2x+1
=x[(x-1)/(x-1)+2/(x-1) ]/(x+1)-x(x+1)(x-1)/(x-1)²
=x/(x-1)-x(x+1)/(x-1)
=-x²/(x-1)
=-(1-x)/(x-1)
=1
3x=2(x+3)
3x=2x+6
∴x=6
检验:x=6是方程的解
(2) x²+x-1=x(x-1)
x²+x-1=x²-x
2x=1
x=1/2
(3)∵x^2+x-1=0
∴x²=1-x
x(1-2/1-x)除(x+1)-x(x^2-1)/x^2-2x+1
=x[(x-1)/(x-1)+2/(x-1) ]/(x+1)-x(x+1)(x-1)/(x-1)²
=x/(x-1)-x(x+1)/(x-1)
=-x²/(x-1)
=-(1-x)/(x-1)
=1
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