# How do you simplify (4x^2 - 12x + 9)/(4x^2 - 9 )?

The numerator is: $4 {x}^{2} - 12 x + 9 = {\left(2 x - 3\right)}^{2}$
The denominator is: $4 {x}^{2} - 9 = \left(2 x + 3\right) \left(2 x - 3\right)$
$\frac{4 {x}^{2} - 12 x + 9}{4 {x}^{2} - 9} = \frac{{\left(2 x - 3\right)}^{\cancel{2}}}{\left(2 x + 3\right) \cancel{\left(2 x - 3\right)}} =$
$= \frac{2 x - 3}{2 x + 3}$