\(A=\left(2x-3\right).\left(3x^2+2x-1\right)-\left(4x+1\right)\cdot\left(x-1\right)\)
\(A=6x^3+4x^2-2x-9x^2-6x+3-\left(4x^2-4x+x-1\right)\)
\(A=6x^3+4x^2-2x-9x^2-6x+3-4x^2+4x-x+1\)
\(A=6x^3-9x^2-5x+4\)
Với \(x=\frac{1}{2}\).Ta có :
\(A=6.\left(\frac{1}{2}\right)^3-9.\left(\frac{1}{2}\right)^2-5.\frac{1}{2}+4\)
\(A=\frac{3}{4}-\frac{9}{4}-\frac{5}{2}+4\)
\(\Rightarrow A=0\)