先化简再求值:x+2分之1-x^2-x分之x^2-4x+4÷(x+1-x-1分之3),其中x是分式方程1⼀x=2⼀x+3的解

2024-11-14 01:25:22
推荐回答(1个)
回答1:

∵2x=x+3 ∴x=3

1/(x+2)-[(x^2-4x+4)/(x^2-x)]/[x+1-3/(x-1)]
=1/(x+2)-[(x-2)^2/(x-1)x]/[(x^2-1-3)/(x-1)]
=1/(x+2)-[(x-2)^2/(x^3-4x)]
=[(x^3-4x)-(x+2)(x-2)^2]/[(x+2)(x^3-4x)]
=(x^2-4)(x-x+2)/(x^2-4)(x^2+2x)
=2/(x^2+2x)

x=3 时,原式=2/(3^2+2*3)=2/(9+6=2/15