To solve an inequality with absolute values on both sides |Is there any difference between X ^ 2-5x + 4 / x ^ 2-4 | 1 and x ^ 2-5x + 4 / | x ^ 2-4 | 1

To solve an inequality with absolute values on both sides |Is there any difference between X ^ 2-5x + 4 / x ^ 2-4 | 1 and x ^ 2-5x + 4 / | x ^ 2-4 | 1

Of course, the two inequalities are the same only when x ^ 2-5x + 4 ≥ 0, that is, X ≤ 1 (and X ≠ - 2) or X ≥ 4. The first inequality | x ^ 2-5x + 4 | / | x ^ 2-4 | - 1 ≤ 0 (| x ^ 2-5x + 4 | - | x ^ 2-4 |) / | x ^ 2-4 | ≤ 0, that is, | x ^ 2-5x + 4 | - | x ^ 2-4 | ≤ 0 and X ≠± 2 are equivalent to the following