Question

〈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

Answer 1

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