Answer:
(608 x - 105 y)/120
Step-by-step explanation:
Simplify the following:
(3 y)/8 - y - 1/3 (x + (3 y)/4) + (5 + 2/5) x
Put each term in (3 y)/4 + x over the common denominator 4: (3 y)/4 + x = (3 y)/4 + (4 x)/4:
(5 + 2/5) x - (((3 y)/4 + (4 x)/4))/3 - y + (3 y)/8
(3 y)/4 + (4 x)/4 = (3 y + 4 x)/4:
(5 + 2/5) x - ((1/4 (3 y + 4 x)))/3 - y + (3 y)/8
4×3 = 12:
(5 + 2/5) x - (3 y + 4 x)/12 - y + (3 y)/8
Put 5 + 2/5 over the common denominator 5. 5 + 2/5 = (5×5)/5 + 2/5:
((5×5)/5 + 2/5) x - (3 y + 4 x)/12 - y + (3 y)/8
5×5 = 25:
(25/5 + 2/5) x - (3 y + 4 x)/12 - y + (3 y)/8
25/5 + 2/5 = (25 + 2)/5:
((25 + 2)/5) x - (3 y + 4 x)/12 - y + (3 y)/8
25 + 2 = 27:
(27 x)/5 - (3 y + 4 x)/12 - y + (3 y)/8
Put each term in (27 x)/5 - (3 y + 4 x)/12 - y + (3 y)/8 over the common denominator 120: (27 x)/5 - (3 y + 4 x)/12 - y + (3 y)/8 = (648 x)/120 + (10 (-3 y - 4 x))/120 - (120 y)/120 + (45 y)/120:
(648 x)/120 + (10 (-3 y - 4 x))/120 - (120 y)/120 + (45 y)/120
(648 x)/120 + (10 (-3 y - 4 x))/120 - (120 y)/120 + (45 y)/120 = (648 x + 10 (-3 y - 4 x) - 120 y + 45 y)/120:
(648 x + 10 (-3 y - 4 x) - 120 y + 45 y)/120
45 y - 120 y = -75 y:
(648 x + 10 (-3 y - 4 x) + -75 y)/120
10 (-3 y - 4 x) = -30 y - 40 x:
(648 x + (-30 y - 40 x) - 75 y)/120
Grouping like terms, -30 y - 75 y + 648 x - 40 x = (648 x - 40 x) + (-30 y - 75 y):
((648 x - 40 x) + (-30 y - 75 y))/120
-30 y - 75 y = -105 y:
(-105 y + (648 x - 40 x))/120
648 x - 40 x = 608 x:
Answer: (608 x - 105 y)/120
