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Determinati elementele urmatoarelor multimi:
A={x∈ multimi zet|[tex] \frac{6}{2x+1} [/tex]∈ multimi zet}
B={x∈ multimi zet|[tex] \frac{-8}{3x-1} [/tex]∈ multimi zet}
C={x∈ multimi zet|[tex] \frac{4x-2}{5x+1} [/tex]∈ multimi zet}
D={x∈ multimi zet[tex] \frac{3x+4}{12x-1} [/tex]∈ multimi numerelor natuirale }


Răspuns :

a) 2x+1 divide 6⇒ 2x+1 ∈D6={1,-1,2,-2,3,-3,6,-6}⇒
2x∈{ 0,-2,1,-3,2,-4,6,-7}⇒x∈{0,-1,1,-2,3}

b) 3x-1 divide -8⇒ 3x-1∈ D(-8)={1,-1,2,-2,4,-4,8,-8}⇒
3x∈{ 2,0,3,1,5,-3,9,-7}⇒x∈{ 0,1,-1,3}

c)semnul " / "= divide
5x+1 / 4x-2 \inmultim cu 5
5x+1 / 5x+1   /inmultim cu 4  

5x+1 /20x -10
5x+1 / 20x+4    scadem de sus in jos si obtinem:
5x+1 / -14 ⇒ 5x+1 ∈D(-14)={1,-1,2,-2,7,-7,14,-14}
5x∈{0,-2,1,-3,6,-8,13,-15}⇒ x∈{0,-3}

d) 12x-1 /3x+4 \inmultim cu 4
    12x-1 / 12x-1
12x-1 / 12x+16
12x-1 /12x-1     , scadem de sus in jos:
12x-1 / 17 ⇒12x-1 ∈D17={1,-1,17,-17}⇒12x∈{2,0,18,-16}⇒x∈{ 0}