[tex]\displaystyle\bf\\\frac{4x^{2} +12x+9}{4x^{2} -9} =\frac{(2x)^{2} +2\cdot 2x\cdot 3+3^{2} }{(2x)^{2} -3^{2} } =\frac{(2x+3)^{2} }{(2x+3)(2x-3)} =\frac{2x+3}{2x-3}[/tex]