Given differential equation is

     (x² - 1)dy/dx + 2xy = 2/(x² - 1)

=> dy/dx + 2xy/(x² - 1) = 2/(x² - 1)² .............1

This is the differential eqaution of the form

dy/dx + Py = Q

Now, IF = e^{∫2x/(x2 - 1) dx}

=> IF = e^{log(x2 - 1)}

=> IF = x² - 1

Multiplying (x² - 1) in equation 1, we get

(x² - 1)dy/dx + 2xy = 2/(x² - 1)

Now, integrate on both side we, get

      y(x² - 1) = ∫2/(x² - 1) dx + C

=> y(x² - 1) = (2/2)*log|(x - 1)/(x + 1)| + C

=> y(x² - 1) = log|(x - 1)/(x + 1)| + C

This is the required solution.