which expression is equivalent to (2/3 x+1/5 y)-(1/6 x-3/4 y)+(5/12 x+2 y)
(2/3 x+1/5 y)-(1/6 x-3/4 y)+(5/12 x+2 y)
(2/3 x+1/5 y)+(-1/6 x+3/4 y)+(5/12 x+2 y)
2/3x-1/6x+5/12+ 1/5y+3/4y+2y
8/12x-2/12x+5/12+4/20y+15/20y+2y
11/12x+59/20y
Simplify the following:
(2 x)/(3)+y/5-(x/6-(3 y)/(4))+(5 x)/(12)+2 y
Put each term in x/6-(3 y)/(4) over the common denominator 12: x/6-(3 y)/(4) = (2 x)/12-(9 y)/12:
(2 x)/(3)+y/5-(2 x)/12-(9 y)/12+(5 x)/(12)+2 y
(2 x)/12-(9 y)/12 = (2 x-9 y)/12:
(2 x)/(3)+y/5-(2 x-9 y)/12+(5 x)/(12)+2 y
Put each term in (2 x)/(3)+y/5-(2 x-9 y)/12+(5 x)/(12)+2 y over the common denominator 60: (2 x)/(3)+y/5-(2 x-9 y)/12+(5 x)/(12)+2 y = (40 x)/60+(12 y)/60+(5 (9 y-2 x))/60+(25 x)/60+(120 y)/60:
(40 x)/60+(12 y)/60+(5 (9 y-2 x))/60+(25 x)/60+(120 y)/60
(40 x)/60+(12 y)/60+(5 (9 y-2 x))/60+(25 x)/60+(120 y)/60 = (40 x+12 y+5 (9 y-2 x)+25 x+120 y)/60:
(40 x+12 y+5 (9 y-2 x)+25 x+120 y)/60
Grouping like terms, 40 x+12 y+5 (9 y-2 x)+25 x+120 y = 5 (9 y-2 x)+(12 y+120 y)+(40 x+25 x):
(5 (9 y-2 x)+(12 y+120 y)+(40 x+25 x))/60
12 y+120 y = 132 y:
(5 (9 y-2 x)+132 y+(40 x+25 x))/60
40 x+25 x = 65 x:
(5 (9 y-2 x)+132 y+65 x)/60
5 (9 y-2 x) = 45 y-10 x:
(45 y-10 x+132 y+65 x)/60
Grouping like terms, -10 x+45 y+132 y+65 x = (45 y+132 y)+(65 x-10 x):
((45 y+132 y)+(65 x-10 x))/60
45 y+132 y = 177 y:
(177 y+(65 x-10 x))/60
65 x-10 x = 55 x:
Answer: | (177 y+55 x)/60
