1)
1−xx+2xx+2+1
1−xx+2xx+2+1=x+2−xx+2x+x+2x+2=2x+22x+2x+2=2x+22(x+1)x+2=2x+2× x+22(x+1)=1x+1x≠−1,x≠−2
2)
(x3y2+x2y+x+y)÷(x2y2−y2x2)
(x3y2+x2y+x+y)÷(x2y2−y2x2)=x3+x2y+xy2+y3y2÷x4−y4x2y2=x2(x+y)+y2(x+y)y2×x2y2(x2−y2)(x2+y2)=(x2+y2)(x+y)y2×x2y2(x2−y2)(x2+y2)=x2(x+y)(x−y)(x+y)=x2x−yx≠0,y≠0,x≠+1,y≠−1
3)
[(n+2n−2)3÷n3+4n2+4n3n2−12n+12]×n3
[(n+2n−2)3÷n3+4n2+4n3n2−12n+12]×n3= [(n+2)3(n−23÷n(n2+4n+4)3(n2−4n+4)]×n3= [(n+2)3(n−23÷n(n+2)23(n−2)2]×n3= (n+2)3(n−2)3×3(n−2)2n(n+2)2×n3=n+2n−2 n≠0,n≠+2,n≠−2
4)
a4−b4a2b2÷[(1+b2a2)×(1−2ab+a2b2)]
a4−b4a2b2÷[(1+b2a2)×(1−2ab+a2b2)]= (a2−b2)(a2+b2)a2b2÷[a2+b2a2×b2−2ab+a2b2]= (a2−b2)(a2+b2)a2b2÷[(a2+b2)×(a−b)2a2b2]= (a2−b2)(a2+b2)a2b2×a2b2(a2+b2)×(a−b)2= (a2−b2)(a−b)2=(a−b)(a+b)(a−b)(a−b)=a+ba−ba≠b,a≠0,b≠0
5)
2a−(2a−3a+1−a2+32a2−2−a+12−2a)×a3+1a2−2
2a−(2a−3a+1−a2+32(a2−1)−a+12(1−a))×a3+1a(a−1)=
2a−(2a−3a+1−a2+32(a−1)(a+1)−a+12(1−a))×a3+1a(a−1)=
2a−(2(a−1)(2a−3)−a2−3+(a+1)(a+1)2(a+1)(a−1))×a3+1a(a−1)=
2a−(2(a2−3a−2a+3)−a2−3+a2+2a+12(a+1)(a−1))×a3+1a(a−1)=
2a−(4a2−10a+6−2+2a2(a+1)(a−1))×a3+1a(a−1)=
2a−4a2−8a+42(a+1)(a−1)×a3+1a(a−1)=
2a−4(a2−2a+1)2(a+1)(a−1)×a3+1a(a−1)=
2a−4(a−1)22(a+1)(a−1)×a3+1a(a−1)=
2a−2(a3+1)a(a+1)=2a2(a+1)−2(a3+1)a(a+1)=
2a3+2a2−2a3−2a(a+1)=2a2−2a(a+1)=
2(a+1)(a−1)a(a+1)=2(a−1)a
x≠−1
x≠0
6)
(1a+1−2aa2−1)×(1a−1)
(1a+1−2aa2−1)×(1a−1)= (a−1)−2a(a+1)(a−1)×1−aa= a−1−2a(a+1)(a−1)×−(a−1)a= −a−1(a+1)(a−1)×−(a−1)a=−(a+1)(a+1)(a−1)×−(a−1)a=1aa≠0,a≠−1,a≠+1
7)
a2+aba2+b2×(aa−b−ba+b)
a2+aba2+b2×(aa−b−ba+b)= a(a+b)a2+b2×(a(a+b)−b(a−b)(a−b)(a+b))= a(a+b)a2+b2×(a2+ab−ab+b2(a−b)(a+b))= a(a+b)a2+b2×(a2+b2(a−b)(a+b))=aa−ba≠+b,a≠−b
8)
[3a8−a3÷4−a24(a2+2a+4)]×a2−4a+4a
[3a8−a3÷4−a24(a2+2a+4)]×a2−4a+4a= 3a(2−a)(4+2a+a2)×4(a2+2a+4)(2−a)(2+a)×a2−4a+4a= 12a(2−a)(2−a)(2+a)×(a−2)2a=122+aa≠0,a≠+2,a≠−2
9)
(4x2−8x+4x2+1÷x+13)÷6x−6x4−1
(4x2−8x+4x2+1÷x+13)÷6x−6x4−1= (2x−2)2x2+1×3x+1×(x2−1)(x2+1)6(x−1)= (2x−2)2x2+1×3x+1×(x−1)(x+1)(x2+1)6(x−1)= 3(2x−2)26=(2x−2)22=4x2−8x+42=2(2x2−4x+22=2x2−4x+2=2(x−1)2x≠+1,x≠−1
10)
6a+(aa−2−aa+2)÷4aa4−2a3+8a−16
6a+a(a+2)−a(a−2)(a−2)(a+2)÷4aa3(a−2)8(a−2)= 6a+a2+2a−a2+2a(a−2)(a+2)×a3(a−2)8(a−2)4a= 6a+4a(a−2)(a+2)×(a−2)(a3+8)4a= 6a+(a−2)(a+2)(a2−2a+4)(a−2)(a+2)=6a+a2−2a+4=a2+4a+4=(a+2)2a≠0,a≠+2,a≠−2