The given fraction is :
[tex]-\frac{3}{2}[/tex]A)
[tex]\begin{gathered} \frac{3}{-2} \\ On\text{ simplify :} \\ \text{negative sign can be writen as :}-\frac{3}{2} \\ \text{-}\frac{3}{2}=-\frac{3}{2} \end{gathered}[/tex]B)
[tex]\begin{gathered} -(\frac{3}{-2}) \\ On\text{ simplify : (-1) }\times(-1)\text{ = +1} \\ \text{ So, }-(\frac{3}{-2})=-(-\frac{3}{2})_{} \\ -(-\frac{3}{2})=\frac{3}{2} \\ \text{Thus, -}\frac{3}{2}\ne\frac{3}{2} \end{gathered}[/tex]C)
[tex]\begin{gathered} \frac{-3}{-2} \\ \text{ On simplify : }\frac{-1}{-1}=1 \\ \text{ So, }\frac{-3}{-2}=\frac{3}{2} \\ \text{-}\frac{3}{2}\ne\frac{3}{2} \end{gathered}[/tex]D)
[tex]\begin{gathered} -(-\frac{3}{2}) \\ On\text{ simplify : (-1) x(-1) = +1} \\ -(-\frac{3}{2})=\frac{3}{2} \\ \text{-}\frac{3}{2}\ne\frac{3}{2} \end{gathered}[/tex]Answer : A)
[tex]\frac{3}{-2}[/tex]