先化简再求值:(x分之-1-x-1分之x-2)除以x方+2x+1分之2x方+1,其中x满足x方-x-1=0

Question

先化简再求值:(x分之-1 -x-1分之x-2)除以x方+2x+1分之2x方+1,其中x满足x方-x-1=0

Answer 1

原式
=(-1/x-(x-2)/(x-1))÷2x^2/(x^2+2x+1)+1
=[(-(x-1)-x(x-2)]/x(x-1)×(x+1)^2/2x^2+1
=(-x+1-x^2+2x)/x(x-1)*(x+1)^2/2x^2+1
=(-x^2+x+1)/(x^2-x)*(x+1)^2/2x^2+1
∵x^2-x-1=0
x^2=x+1
x^2-x=1
=(-1+1)/1*x^4/2x^2+1
=0+1
=1
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