To simplify the given expression:

Distribute the 3x^2 and the -38 in the numerator:
3x^2 - 38

Factor the denominator by recognizing that it is a difference of squares:
x^2 - 1 = (x + 1)(x - 1)

Combine like terms in the numerator and factor the denominator:
3x^2 - 38 / (x + 1)(x - 1) - x - 4 / 2(x - 1) - 7 / x + 1 = 0

Find a common denominator for the fractions:
(3x^2 - 38)(x - 1) - x(x + 1)(x - 1) - 4(x + 1) - 7(2)(x + 1) = 0

Simplify the expression and solve for x:
3x^3 - 3x^2 - 38x + 38 - x^3 - x^2 + x - 4 - 14x -7 = 0
2x^3 - 4x^2 - 52x + 27 =0

This is your simplified expression. Now you can solve for x using methods like factoring, the quadratic formula, or other methods.