For x > 1 and x < -1, we can multiply by the product of the denominators to get
2(x+1) > 7(x-1)
9 > 5x
x < 9/5
For -1 < x < 1, we can do the same, but we must reverse the sense of the inequality.
2(x+1) < 7(x-1)
9 < 5x
x > 1.8
A graph confirms the solution is
-∞ < x < -1 ∪ 1 < x < 1.8
