(1)
(x^2-2x+1)/x^2
=(x-1)^2/x^2
=[(x-1)/x]^2
(2)
2/(2a+3)+3/(2a-3)+(2a+15)/(4a^2-9)
=2(2a-3)/(4a^2-9)+3(2a+3)/(4a^2-9)+(2a+15)/(4a^2-9)
=(4a+18)/(4a^2-9)
(3)
(x^2-2x+1)/(x^2-1)÷(x-1)/(x^2+x)
=(x-1)^2/[(x+1)(x-1)]÷(x-1)/[x(x+1)]
=(x-1)/(x+1)÷(x-1)/[x(x+1)]
=(x-1)*x(x+1)/[(x+1)(x-1)]
=x