There are multiple ways of doing this. I'll just show you one of the simpler ones for now.
Multiply both sides of the inequality by the denominator squared. In this case (1-y)². This ensures that the denominator is not neglected.
You will get (1+y)(1-y) > 0
Now solve for y. These are the 'starting points' of the range. Check both sides of your solutions on the number line to see which side satisfies the inequality (whether the the inequality holds true for y values < the solution or > solution)
Combine the two solutions to form one that satisfies both of your solutions. For example if you get y > 6 and y < 10, your combined solution is 6 < y < 10. There are some times when you won't be able to combine them. For example y < 6 and y > 10. In this case just write the two solutions down.