先化简,再求值

( a" - 1 ) /( a - 1 ) - √( a" + 2a + 1 ) /( a" + a ) - 1/a
= [ ( a" - 1" ) /( a - 1 ) ] - [ √( a + 1 )" /( a + 1 )a ] - 1/a
注意,开方之后必须是正数
= [ ( a + 1 )( a - 1 ) /( a - 1 ) ] - [ | a + 1 | /( a + 1 )a ] - 1/a
= ( a + 1 ) + [ ( a + 1 ) /( a + 1 )a ] - 1/a
由于 a = -1 - √3 ,a+1 < 0 ,
这样,| a + 1 | 就必须是 - ( a + 1 ) ,
接下来
= a + 1 + 1/a - 1/a
= a + 1
= -1 - √3 + 1
= - √3

原式=(a+1)(a-1)/(a-1)-[(a+1)^2]^(-1/2)/[a(a+1)]-1/a
=a+1+(a+1)/[a(a+1)]-1/a
=a+1+1/a-1/a
=a+1

原式=(a+1)(a-1)/(a-1)-|a+1|/a(a+1)-1/a=-√3+1/a-1/a=-√3