Question

Se considera multimile A={x ∈Ζ | $\frac{4x+9}{3x-2}$ ∈ Ζ}  si B={x∈Ζ|$\frac{9x+20}{2x+3}$ ∈Ζ} Sa se afle elementele lor . 

Answer 1

[tex] \frac{4x+9}{3x-2} \in Z<=>3 \cdot \frac{4x+9}{3x-2} \in Z<=>\frac{12x+27}{3x-2} \in Z<=>\\ \frac{4(3x-2)+35}{3x-2} \in Z<=>4+\frac{35}{3x-2} \in Z<=>\frac{35}{3x-2} \in Z<=>\\ (3x-2)\in D_{35}=\{\pm1,\pm5,\pm7,\pm35\}\\ 3x-2=1=>x=1\in Z\\ 3x-2=-1=>x=\frac{1}{3}\notin Z\\ 3x-2=5=>x=\frac{7}{3}\notin Z\\ 3x-2=-5=>x=-1\in Z\\ 3x-2=7=>x=3\in Z\\ 3x-2=-7=>x=-\frac{5}{3}\notin Z\\ 3x-2=35=>x=\frac{37}{3}\notin Z\\ 3x-2=-35=>x=-11\in Z[/tex]
A={1,-1,3,-11}
Analog se deterina multimea B.