Question

F(x)=6x la a2-a -7x-3 supra 2x la a doua +x-6
F(a) € Z a=?

Answer 1

F(x)=$\frac{6 x^{2} -7x-3}{2 x^{2} +x-6}$

Observam ca fractia se mai scrie:

F(x)=$\frac{(3x+1)(2x-3)}{(x+2)(2x-3)}$

F(x)=$\frac{3x+1}{x+2}$

F(x)=$\frac{3x+6-5}{x+2}$

F(x)=$\frac{3(x+2)-5}{x+2}$

F(x)=3 - $\frac{5}{x+2}$

Pentru ca F(a)∈Z trebuie ca (x+2) | 5, adica (a+2)∈{-5, -1, 1, 5}, de unde obtinem a∈{-7, -3, -1, 3}.