先化简,再求值.(x-1)/(x-2)·(x²-4)/(x²-2x+1)÷1/(x²-1)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/21 20:33:39
先化简,再求值.(x-1)/(x-2)·(x²-4)/(x²-2x+1)÷1/(x²-1),其中x²-x=10
(x-1)/(x-2) ·(x²-4)/(x²-2x+1)÷1/(x²-1)
=(x-1)/(x-2) · (x-2)(x+2)/(x-1)² ÷ 1/(x-1)(x+1)
=(x+2)/(x-1) ÷ 1/(x-1)(x+1)
=(x+2)(x+1)
=x²+3x+2
∵ x² - x =10,配方得:
( x-1/2)²=10+1/4
解得:x=(√41+1)/2,或 x=(√41-1)/2
代入上式,得:
① 当 x=(√41+1)/2 时,
[(√41+1)/2]²+3×(√41+1)/2+2=14+2√41;
② 当 x=(√41-1)/2 时,
[(√41-1)/2]²+3×(√41-1)/2+2=11+√41.
.不懂的地方追问吧
=(x-1)/(x-2) · (x-2)(x+2)/(x-1)² ÷ 1/(x-1)(x+1)
=(x+2)/(x-1) ÷ 1/(x-1)(x+1)
=(x+2)(x+1)
=x²+3x+2
∵ x² - x =10,配方得:
( x-1/2)²=10+1/4
解得:x=(√41+1)/2,或 x=(√41-1)/2
代入上式,得:
① 当 x=(√41+1)/2 时,
[(√41+1)/2]²+3×(√41+1)/2+2=14+2√41;
② 当 x=(√41-1)/2 时,
[(√41-1)/2]²+3×(√41-1)/2+2=11+√41.
.不懂的地方追问吧
先化简,再求值:[(x-2/x²+2x)-(x-1/x²+4x+4)]÷﹙x-4/x+2﹚,其中x&
先化简,再求值:(1)(x+1/x²-x-x/x²-2x+1)÷1/x,x=根号2+1
先化简,再求值:(x²+2x分之x-2-x²+4x+4分之x-1)÷x+2分之x-4,其中x
先化简再求值:(x+2/x²-2x - x-1/x²-4x+4)÷ x-4/x,其中x=3/2
先化简,再求值:(3x+4/x²-1-2/x-1)÷x+2/x²-2x+1
先化简,再求值:x+1/x除以(x- 1+x²/2x),其中x=根号2+1
先化简,再求值:(x²-1分之x-3)÷(x²+2x+1分之x²)-(2x-3-x+1分之
先化简再求值:(x²-4x+4分之x+8-2-x分之1)÷x²-2x分之x+3 x²-4=
化简求值 (x³+4x²)÷x+(2x+1)(2x-1)-4x(x+1) x=-2
先化简代数式再求值(3/x+1 - x+1)÷x²-2x/x+1,其中x满足方程x/x-1+1/x=1
先化简,再求值:[x+2/(x^2-2x)-(x-1)/(x^2-4x+4)]÷2x-8/(x^3-2x^2)
先化简,再求值:(4x²-3x)-2(x²+2x-1)-(x²+x-1)