Question

先化简再求值(x^2-1分之x^2-2x+1+x分之1)÷x+1分之1,其中x=-2

Answer 1

/ 表示分数线

原式={[(x²-2x+1)/(x²-1)]+1/x}÷[1/(x+1)]

={[(x-1)²]/[(x+1)(x-1)]+1/x}×(x+1)

={[(x-1)/(x+1)]+1/x}×(x+1)

=[(x-1)/(x+1)]×(x+1)+[(x+1)/x]

=(x-1)+[(x+1)/x]

=[x(x-1)+(x+1)]/x

=(x²-x+x+1)/x

=(x²+1)/x

当x=-2时

原式=[(-2)²+1]/(-2)

=(4+1)/(-2)

= -5/2