Simplify:

5/4x-8y-1/4x+7y+3

A) x-y+3

B) 3/2x+y+3

C) 3/2x-y+3

D) x+y+3

A) x-y+3 is your answer

Proof:

(5 x) / 4 - 8 y - x/4 + 7 y + 3

Put each term in (5 x) / 4 - 8 y - x/4 + 7 y + 3 over the common denominator 4: (5 x) / 4 - 8 y - x/4 + 7 y + 3 = (5 x) / 4 - (32 y) / 4 - (x) / 4 + (28 y) / 4 + 12/4:

(5 x) / 4 - (32 y) / 4 - x/4 + (28 y) / 4 + 12/4

(5 x) / 4 - (32 y) / 4 - x/4 + (28 y) / 4 + 12/4 = (5 x - 32 y - x + 28 y + 12) / 4:

(5 x - 32 y - x + 28 y + 12) / 4

Grouping like terms, 5 x - 32 y - x + 28 y + 12 = (28 y - 32 y) + (5 x - x) + 12:

((28 y - 32 y) + (5 x - x) + 12) / 4

28 y - 32 y = - 4 y:

(-4 y + (5 x - x) + 12) / 4

5 x - x = 4 x:

(-4 y + 4 x + 12) / 4

Factor 4 out of - 4 y + 4 x + 12:

(4 (-y + x + 3)) / 4

(4 (-y + x + 3)) / 4 = 4/4 * (3 + x - y) = 3 + x - y:

Answer: 3 + x - y