Question

Va rog mult sa ma ajutati. Este urgent

Answer 1

(4x-2)/(5x+1) ∈ Z ⇒ (5x+1) | (4x-2)

(5x+1) | (5x+1) ⇒ (5x+1) | 4(5x+1) = 20x + 4    (relatia 1)
(5x+1) | (4x-2) ⇒ (5x+1) | 5(4x-2) = 20x - 10     (relatia 2)

⇒ (5x+1) | [(relatia 1) - (relatia 2)] = 14     adica 20x+4-20x+10=14

⇒(5x +1) ∈ {-14,-7,-2,-1,1,2,7,14}

5x ∈{-15,-8,-3,-2,0,1,6,13}   

C = {-3,0} 

(3x+4)/(12x-1) ∈ N  ⇒ (12x - 1) | ((3x+4)     
          
(12x-1) | (3x+4) ⇒ (12x-1) | 4(3x +4) = 12x + 16    (relatia 1)

(12x-1) |  (12x-1)    (relatia 2)

⇒ (12x-1) | [(relatia 1) - (relatia 2)] = 17    adica 12x+16-12x+1=17

12x - 1 ∈ {-7,-1,1,17}   

12x ∈ {-6,0,2,18}
D={0}