〈x-1分之3x减x+1〉乘x分之x减一,其中x等于根号2减2,先化减再求值_数学解答

〈x-1分之3x减x+1〉乘x分之x减一,其中x等于根号2减2,先化减再求值

人气：365 ℃　时间：2020-04-01 12:53:03

解答

原式=[3x /(x-1) - x + 1] * (x-1)/x
=3 - (x-1) + (x-1)/x
= 4-x + (x-1)/x
=4-x +1- 1/x
=5 - x - 1/x
代入x=√2 - 2
原式=5 - (√2 - 2) - 1/(√2 - 2)
=7 - √2 - (√2 + 2) /(√2 - 2) (√2 + 2)
=7 - √2 - (√2 + 2) /(-2)
=7 - √2 + √2/2 +1
=8 - √2/2