Simplify the following:
(2 (6 a+3 b))/(3)-(a-2 b)/(2)
Put each term in (2 (6 a+3 b))/3-(a-2 b)/2 over the common denominator 6: (2 (6 a+3 b))/3-(a-2 b)/2 = (4 (6 a+3 b))/6+(3 (2 b-a))/6:
(4 (6 a+3 b))/6+(3 (2 b-a))/6
(4 (6 a+3 b))/6+(3 (2 b-a))/6 = (4 (6 a+3 b)+3 (2 b-a))/6:
(4 (6 a+3 b)+3 (2 b-a))/6
4 (6 a+3 b) = 24 a+12 b:
(24 a+12 b+3 (2 b-a))/6
3 (2 b-a) = 6 b-3 a:
(24 a+12 b+6 b-3 a)/6
Grouping like terms, 24 a+12 b-3 a+6 b = (12 b+6 b)+(24 a-3 a):
((12 b+6 b)+(24 a-3 a))/6
12 b+6 b = 18 b:
(18 b+(24 a-3 a))/6
24 a-3 a = 21 a:
(18 b+21 a)/6
Factor 3 out of 18 b+21 a:
3 (6 b+7 a)/6
3/6 = 3/(3×2) = 1/2:
Answer: |
| (7a+6b)/2
