x2?92(x?2)(x?3)(x?3)2(x?2)?? ===2x+6. x?2x?3x?3x?2当x=2?3时,原式=2(2?3)+6=22. 5.先化简再求值:(x41?)?2,其中x?2. x?22?xx?2x2 x241?)?2解:(x?22?xx?2x x2?41(x?2)(x?2)11=???? x?2x(x?2)x?2x(x?2)x当x?2时,原式12?2. 2 x?yx2?y26.先简化,再求值:,其中?x?2yx2?4xy?4y2x?y(x?2y)2x?2yx?yx2?y2解:= ???22x?yx?2yx?4xy?4yx?2y(x?y)(x?y)当时,原式=1?2?2(1?2)1?2?1?2?32?1 2 x?x?1?17.先化简,再求值:?2?2??,其中x?2?1. ?x?xx?2x?1?x?x?1x?1??x解:原式??????6分 ???22xx?1??x?1????x?1????当x?2?1时,原式??1?2?2??1???????10分 2 8. 先化简,再求值:(解:原式=(2aa?)÷a,其中a=2?1. a?11?a12aaa1)÷a=×= -aa-1a-1a-1a-1当a=2?1时,原式=1121===. a-12+1-1229.先化间,再求值:(1?11)?2?(x?2),其中x?6. x?1x?1 13
解:原式=当x?x?1?1?(x?1)(x?1)?(x?2)=x(x?1)?(x?2)=x2?2 x?16时,原式=(6)2?2=4. 2?a?a?210.先化简,再求代数式的值:? , 其中a?3?1. ???2?1?aa?1?1?a解:原式=(?a?221?aa?22?1?a?)?? =??(1?a)(1?a)a?1???a a1?a2a?1??a?22(1?a)3? =-----------------------------4分 a?1a(a?1)a(a?1) =当a?3?1时 原式=33?1?1?33?3----------------------------------------------6分 a2?b22ab?b2?(a?),其中a=2?1,b=1 11.先化简,再求值:2aa?ab(a?b)(a?b)(a?b)2112解:原式= = = ??a?ba(a?b)a2?1?12x22xx?12.先化简,再求值()÷,其中x=3+1. x?1x?11?xx22xxx22xx?1(?)??(?)?解: x?11?xx?1x?1x?1xx2?2xx?1x(x?2)x?1?x?2 ??? =x?1xx?1x当x?3?1时,原式=3?1?2?13. 先化简,再求值:解:原式? 3?3 1a?1a?1?2?,其中a?2. a?1a?2a?1a?1????3分 1a?1a?1 ??2a?1(a?1)a?1 ?11? a?1a?1????4分 14
??2 a2?1 ????7分 当a?2时,原式??2(2)?12??2 ????9分 14.先化简,再求值. x?1x2?xx?6?2?其中x=3 x?6x?36x解:原式=x?1(x?6)(x?6)x?6x?6x?612? = =. ??xxxx?6x(x?1)x123?43 当x=3时,原式=2a?2a2?1??a?1??215.先化简再求值a?1a?2a?1 其中a=3?1 2a?2a2?1??a?1??2解: a?1a?2a?1=2(a?1)1(a?1)(a?1)2a?1a?3???== 2a?1a?1a?1a?1a?1(a?1)3?1?33?43?43??3 3把a?3?1代人上式中,得原式=3?1?1 16. 先化简,再求值:x( 11?),其中x?5?1. xx?1解:x(?1x1x?1?x115)?x??,当x?5?1,原式=. ?x?1x(x?1)x?15?1?152aa?)÷a,其中a=2?1. a?11?a 17.先化简,再求值:(解:原式=(12aaa1)÷a=×= -aa-1a-1a-1a-1当a=2?1时,原式=1121===. a-12+1-122 15
18.先化简,再求值: (x— x1)÷(1+2),其中x=3—1. x?1x?1??????2分 2x(x?1)?x?1?1x解: 原式=÷2x?1x?1 = x2 ×(x?1)(x?1)x?1x2 ??4分 = x-1 ??5分 ∵x = 3-1, ∴原式= 3-1-1=3-2 ??????6分 19.先化简,再求值:a?2a?1a?,其中a=3+1. a2?1a?12 (a?1)2a解:原式=????????3分 ?(a?1)(a?1)a?1 =a?1a1?=??????4分 a?1a?1a?1当a?3?1时,原式=20. 先化简,再求值:13=??????5分 33 xy?,其中x?2?1,y?2?1. y(x?y)x(x?y)22xy解:原式= ??????1分 ?xy?x?y?xy?x?y?x2?y2= ?????2分 xy?x?y?=(x?y)(x?y)???????3分 xy?x?y? =x?y???????4分 xy 当 x?2?1,y?2?1时, 16