+1094 (x+1)/(x-2)≥(x+3)/(x-4)
Move the right to the left:
(x + 1) / (x - 2) - (x + 3) / (x - 4) >= 0
Find the LCD:
(x + 1)(x - 4) / (x - 2)(x - 4) - (x + 3)(x - 2) / (x - 4)(x - 2) >= 0
Combine the two fractions:
(x + 1)(x - 4) - (x + 3)(x - 2) / (x - 4)(x - 2) >= 0
Multiply both sides by (x - 4)(x - 2):
(x + 1)(x - 4) - (x + 3)(x - 2) >= 0
Expand:
x^2 - 3x - 4 - (x^2 + x - 6) >= 0
Distribute negative:
x^2 - 3x - 4 - x^2 - x + 6 >= 0
Combine like terms:
-4x + 2 >= 0
Subtract 2:
- 4x >= -2
Divide - 4:
x <= 1/2
:)
