(1) (x+3)^2-(x-1)(x-2)
=x^2+6x+9-(x^2-3x+2)
=x^2+6x+9-x^2+3x-2
=x^2-x^2+6x+3x+9-2
=9x+7
(2)(a^2-1)÷(1-1/a)
=(a^2-1)÷(a-1)/a
=(a-1)(a+1)×a/(a-1)
=a(a+1)
=a^2+a
(3)(x+y)^2-(x^3-y^3)除以(x-y)
=(x+y)^2-(x-y)(x^2+xy+y^2)×1/(x-y)
=(x+y)^2-(x^2+xy+y^2)
=x^2+2xy+y^2-x^2-xy-y^2
=xy
{3x^2(a^2+b^2)-3a^2b^2+3[x^2+(a+b)x+ab]*[x(x-a)-b(x-a)]}除以2x^2
={3x^2(a^2+b^2)-3a^2b^2+3[(x+a)(x+b)]*[(x-b)(x-a)]}除以2x^2
={3x^2(a^2+b^2)-3a^2b^2+3[(x+a)(x-a)]*[(x-b)(x+b)]}除以2x^2
={3x^2(a^2+b^2)-3a^2b^2+3[(x^2-a^2)]*[(x^2-b^2)]}除以2x^2
={3x^2(a^2+b^2)-3a^2b^2+3[x^4-(a^2+b^2)x^2+a^2b^2]}除以2x^2
={3x^2(a^2+b^2)-3a^2b^2+3x^4-3(a^2+b^2)x^2+3a^2b^2]}除以2x^2
=3x^4除以2x^2
=3x^2/2
=3*2^2/2
=12/2
=6