Răspuns:
Explicație pas cu pas:
[tex]\frac{5x+7}{2x+1}=\frac{4x+2+x+5}{2x+1}=\frac{2(2x+1)}{2x+1}+\frac{x+5}{2x+1} =2+\frac{x+5}{2x+1}~ apartine~N\\[/tex]
Deci 2x+1 este un divizor natural a lui x+5. ⇒2x+1≤x+5, ⇒x≤4
Prin probe gasim ca x∈{0,1,4}. Deci card A=3.
La multimea B expresia e aceeasi,
x∈{-5,-2, -1, 0,1,4}, deci card B=6.
[tex]\frac{7x+1}{x-9}=\frac{7x-63+1+63}{x-9}=\frac{7(x-9)}{x-9} +\frac{64}{x-9}=7+ \frac{64}{x-9}\\[/tex]
Pentru x natural, x-9 trebuie sa fie un divizor intreg a lui 64.
x-9∈{-64, -32, -16, -8, -4, -2, -1, 1,2,4,8,16,32,64}, adunand 9, obtinem
x∈{-55,-23, -7,1, 5,7,8,10,11,13,17,25,41,73}, deoarece x∈N, ⇒
x∈{1, 5,7,8,10,11,13,17,25,41,73}, atunci card C=11.
[tex]\frac{4x+9}{3x-1}=\frac{3x-1+1+x+9}{3x-1}=1+\frac{x+10}{3x-1}[/tex]
Prin probe gasim ca x∈{-10}, deci card D=1.
