b) Để phân thức đó là số nguyên thì :
\(3x^2-x+3⋮3x+2\)
\(3x^2+2x-3x-2+5⋮3x+2\)
\(x\left(3x+2\right)-\left(3x+2\right)+5⋮3x+2\)
\(\left(3x+2\right)\left(x-1\right)+5⋮3x+2\)
Mà \(\left(3x+2\right)\left(x-1\right)⋮3x+2\)
\(\Rightarrow5⋮3x+2\)
\(\Rightarrow3x+2\inƯ\left(5\right)=\left\{1;5;-1;-5\right\}\)
\(\Rightarrow x\in\left\{-\dfrac{1}{3};1;-1;-\dfrac{7}{3}\right\}\)
Mà x nguyên \(\Rightarrow x\in\left\{1;-1\right\}\)
Vậy..........
a) Để phân thức đó là số nguyên thì :
\(2x^3+x^2+2x+8⋮2x+1\)
\(2x^3+x^2+2x+1+7⋮2x+1\)
\(x^2\left(2x+1\right)+\left(2x+1\right)+7⋮2x+1\)
\(\left(2x+1\right)\left(x^2+1\right)+7⋮2x+1\)
Mà \(\left(2x+1\right)\left(x^2+1\right)⋮2x+1\)
\(\Rightarrow7⋮2x+1\)
\(\Rightarrow2x+1\inƯ\left(7\right)=\left\{1;7;-1;-7\right\}\)
\(\Rightarrow x\in\left\{0;3;-1;-4\right\}\)
Vậy..........
