Question

先化简，再求值。x+1分之x的平方-x乘x的平方-2x+1分之x的平方-1，其中x的平方-3x+2=0

Answer 1

x的平方-3x+2=0
(x-2)(x-1)=0
∴x=2或x=1

x+1分之x的平方-x乘x的平方-2x+1分之x的平方-1
=x(x-1)/(x+1)× (x+1)(x-1)/(x-1)²
=x
=2或1

Answer 2

x²-3x+2=0
(x-1)(x-2)=0
∴x=1或x=2
x+1分之x的平方-x乘x的平方-2x+1分之x的平方-1
=(x²-x)/(x+1)*(x²-1)/(x²-1)²
=x(x-1)(x-1)(x+1)/[(x+1)(x-1)²]
=x
∵x=1
分式无意义
∴原式的值=2

Answer 3

(x^2-x)/(x+1)*(x^2-1)/(x^2-2x+1)
=x(x-1)^2/(x-1)^2
=x
x^2-3x+2=0
(x-1)(x-2)=0
x=1 x=2