Simplify the following:
(x-3)/3+(4-x)/4
Put each term in (x-3)/3+(4-x)/4 over the common denominator 12: (x-3)/3+(4-x)/4 = (4 (x-3))/12+(3 (4-x))/12:
(4 (x-3))/12+(3 (4-x))/12
(4 (x-3))/12+(3 (4-x))/12 = (4 (x-3)+3 (4-x))/12:
(4 (x-3)+3 (4-x))/12
4 (x-3) = 4 x-12:
(4 x-12+3 (4-x))/12
3 (4-x) = 12-3 x:
(-12+4 x+12-3 x)/12
Grouping like terms, -12+4 x+12-3 x = (4 x-3 x)+(12-12):
((4 x-3 x)+(12-12))/12
4 x-3 x = x:
(x+(12-12))/12
12-12 = 0:
Answer: | x/12
