Given data:
The given expression can be wriiten as,
[tex]\begin{gathered} \frac{9x^2+12x+4}{4x^2-27x-7}\div\frac{12x^2+5x-2}{16x^2-1}=\frac{(3x+2)^2}{4x^2-28x+x-7}\div\frac{12x^2+8x-3x-2}{(4x-1)(4x+1)} \\ =\frac{(3x+2)(3x+2)}{(x-7)(4x+1)}\div\frac{(3x+2)(4x-1)}{(4x-1)(4x+1)} \\ =\frac{(3x+2)(3x+2)}{(x-7)(4x+1)}\div\frac{(3x+2)}{(4x+1)} \\ =\frac{(3x+2)(3x+2)}{(x-7)(4x+1)}\times\frac{(4x+1)}{(3x+2)} \\ =\frac{3x+2}{x-7} \end{gathered}[/tex]Thus, the simplification of the given expression is (3x+2)/(x-7), so option (A) is correct.
