1.(x-3)/(x^2-1)-2/(1+x)
=(x-3)/(x+1)(x-1)-2(x-1)/(x+1)(x-1)
=(x-3-2x+2)/(x+1)(x-1)
=(-x-1)/(x+1)(x-1)
=-(x+1)/(x+1)(x-1)
=-1/(x-1)
2.2x+2+5/(x-1)
=[2(x+1)(x-1)+5]/(x-1)
=(2x^2-2+5)/(x-1)
=(2x^2+3)/(x-1)
3.x/(x^2-25)-5/(x^2+10x+25)
=x/(x+5)(x-5)-5/(x+5)^2
=[x(x+5)-5(x-5)]/(x+5)^2(x-5)
=(x^2+5x-5x+25)/(x+5)^2(x-5)
=(x^2+25)/(x+5)^2(x-5)
4.2xy/(x^2-y^2)+x/(x+y)-y/(y-x)
=2xy/(x+y)(x-y)+x(x-y)/(x+y)(x-y)+y(x+y)/(x+y)(x-y)
=(2xy+x^2-xy+xy+y^2)/(x+y)(x-y)
=(x^2+y^2+2xy)/(x+y)(x-y)
=(x+y)^2/(x+y)(x-y)
=(x+y)/(x-y)
5.(a-1)/a/(a-1/a)
=[(a-1)/a]/(a^2-1)/a]
=(a-1)/(a+1)(a-1)
=1/(a+1)
=1/(2+1)
=1/3