先化简,再求值:X^2-4X+4⼀X^2+X⼀(3⼀X+1-X+1)+1⼀X+2,其中X为方程X^2+2X-1=0的解

2024-12-15 07:07:21
推荐回答(1个)
回答1:

(X^2-4X+4)/(X^2+X)÷[3/(X+1) -X+1] + 1/(X+2)
=(x-2)²/[x(x+1)] ÷[(3-x²+1)/(x+1)] + 1/(X+2)
=(x-2)²/[x(x+1)] *(x+1)/[-(x+2)(x-2)] + 1/(X+2)
=(x-2)/[-x(x+2)] + 1/(x+2)
=(-x+2+x)/[x(x+2)]
=2/(x²+2x)
若x为方程x²+2x-1=0的解,那么:x²+2x=1
所以:
所求式子=2/(x²+2x)=2/1=2