（a-1/a+1）÷ a^2-2a/a^2-4 × a+1/a^2+3a+2
=（a-1/a+1）* （a+2)(a-2)/ a(a-2) × a+1/(a+1)(a+2)
=（a-1)(a+2)/a(a+1)(a+2)
=（a-1)/ a(a+1)