2/(x-1) ÷(2/(x^2-1) + 1/(x+1))
=2/(x-1)÷(2/(x+1)(x-1)+ 1/(x+1))
=2/(x-1)÷(2+x-1)/(x+1)(x-1)
=2/(x-1)÷(x+1)/(x+1)(x-1)
=2/(x-1)÷1/(x-1)
=2
2/(x-1) ÷(2/(x^2-1) + 1/(x+1))
=2/(x-1)÷(2/(x+1)(x-1)+ 1/(x+1))
=2/(x-1)÷(2+x-1)/(x+1)(x-1)
=2/(x-1)÷(x+1)/(x+1)(x-1)
=2/(x-1)÷1/(x-1)
=2