Question

determinati multimea A = {x apartine N|x+2/2x-3 apartine N

Answer 1

2x-3 divide pe x+2
2x-3 divide pe 2(x+2)=2x+4
deci (2x+4)/(2x-3)∈N
 (2x-3+7)/(2x-3)∈N
(2x-3)/(2x-3) +7/(2x-3)∈N
1+7/(2x-3)∈N
dar 1 ∈N
deci 7/(2x+3)∈N
2x-3∈D7={1;7}
2x-3=1  2x=4    x=2∈N

2x-3=7  2x=10  x=5∈N

deci x∈{2;5}
verificare (2+2)/(4-3)=4/1=4∈N
                 (5+2)/ (10-3)=7/7=1∈N, problema este bine rezolvata