+23246 (4x² - 16x + 7) / (x² - 4x + 4) > 3
Multiply both sides by x² - 4x + 4:
4x² - 16x + 7 > 3(x² - 4x + 4)
4x² - 16x + 7 > 3x² - 12x + 12
Subtract 3x² - 6x + 12 from both sides:
x² - 4x - 5 > 0
(x - 5)(x + 1) > 0
Either both x - 5 and x + 1 are positive or both x - 5 and x + 1 are negative.
If x - 5 > 0 and x + 1 > 0 ---> x > 5 and x > -1 ---> x > 5
If x - 5 < 0 and x + 1 < 0 ---> x < 5 and x < -1 ---> x < -1
Answer: x < -1 or x > 5
+23246 (4x² - 16x + 7) / (x² - 4x + 4) > 3
Multiply both sides by x² - 4x + 4:
4x² - 16x + 7 > 3(x² - 4x + 4)
4x² - 16x + 7 > 3x² - 12x + 12
Subtract 3x² - 6x + 12 from both sides:
x² - 4x - 5 > 0
(x - 5)(x + 1) > 0
Either both x - 5 and x + 1 are positive or both x - 5 and x + 1 are negative.
If x - 5 > 0 and x + 1 > 0 ---> x > 5 and x > -1 ---> x > 5
If x - 5 < 0 and x + 1 < 0 ---> x < 5 and x < -1 ---> x < -1
Answer: x < -1 or x > 5
