a: \(F=\dfrac{3x^3-x^2-6x^2+2x+3x-1}{2x^3+3x^2-4x^2-6x+2x+3}\)
\(=\dfrac{\left(3x-1\right)\left(x^2-2x+1\right)}{\left(2x+3\right)\left(x^2-2x+1\right)}=\dfrac{3x-1}{2x+3}\)
b: Để 6x-2/(2x+3)^2 là số nguyên thì \(6x-2⋮4x^2+12x+9\)
=>12x^2-4x chia hết cho 4x^2+12x+9
=>12x^2+36x+27-40x-27 chia hết cho 4x^2+12x+9
=>-40x^2-27x chia hết cho 4x^2+12x+9
=>x=0