2x-3 over 18 - 2x+1 over 6 =
(2x - 3) / 18 - (2x+1)/6 =
Simplify the following:
(2 x-3)/18+(-1-2 x)/6
Put each term in (2 x-3)/18+(-1-2 x)/6 over the common denominator 18: (2 x-3)/18+(-1-2 x)/6 = (2 x-3)/18+(3 (-1-2 x))/18:
(2 x-3)/18+(3 (-1-2 x))/18
(2 x-3)/18+(3 (-1-2 x))/18 = ((2 x-3)+3 (-1-2 x))/18:
(-3+2 x+3 (-1-2 x))/18
3 (-1-2 x) = -3-6 x:
(2 x+-3-6 x-3)/18
Grouping like terms, 2 x-6 x-3-3 = (2 x-6 x)+(-3-3):
((2 x-6 x)+(-3-3))/18
2 x-6 x = -4 x:
(-4 x+(-3-3))/18
-3-3 = -6:
(-6-4 x)/18
Factor -2 out of -4 x-6:
-2 (2 x+3)/18
The gcd of -2 and 18 is 2, so (-2 (2 x+3))/18 = ((2 (-1)) (2 x+3))/(2×9) = 2/2×(-(2 x+3))/9 = (-(2 x+3))/9:
Answer: | (-1 (2x+3))/9
