[tex]\begin{gathered} \frac{6x^2+7x-3}{4x^2-9} \\ 6x^2+7x-3=(2x+3)(3x-1) \\ 4x^2-9=(2x+3)(2x-3) \\ \frac{6x^2+7x-3}{4x^2-9}=\frac{(2x+3)(3x-1)}{(2x+3)(2x-3)}=\frac{3x-1}{2x-3} \\ \frac{6x^2+7x-3}{4x^2-9}=\frac{3x-1}{2x-3} \\ \text{The expression }\frac{6x^2+7x-3}{4x^2-9}\text{ in lowest terms is }\frac{3x-1}{2x-3} \\ To\text{ determine when is undefined} \\ 2x-3=0 \\ 2x=3 \\ x=\frac{3}{2} \\ The\text{ expression is undefined when x is }\frac{3}{2} \end{gathered}[/tex]
