作业帮先化简,再求值
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/07/08 09:11:27
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
= [ ( 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