a-1+1/a+1
=[(a-1)(a+1)+1]/(a+1)
=(a^2-1+1)/(a+1)
=a^2/(a+1)
1/2axy+2/3bx^2-3/4xy^2
=(6bxy+8ay^2-9abx)/(12abx^2y^2)
1/（4x^2-4y^2）+（3x）/（2x^2-4xy^2+2y^2）
=1/4(x-y)(x+y)+3x/2(x-y)^2
=[(x-y)+6x(x+y)]/[4(x+y)(x-y)^2]
=(x-y+6x^2+6xy)/[4(x+y)(x-y)^2]
（x+2）/（x-2）—(x^2+2x)/（x^2-4）
=(x^2+4x+4-x^2-2x)/x+2)(x-2)
=(2x+4)/x+2)(x-2)
=2/(x-2)