Given rational expression is:
[tex]\frac{(4x^2-32x+48)}{(3x^2-17x-6)}[/tex]
Now we can simplify this by factoring as shown below:
[tex]=\frac{4(x^2-8x+12)}{(3x^2-17x-6)}[/tex]
[tex]=\frac{4(x-2)\left(x-6\right)}{(3x^2-18x+1x-6)}[/tex]
[tex]=\frac{4(x-2)\left(x-6\right)}{3x\left(x-6\right)+1\left(x-6\right)}[/tex]
[tex]=\frac{4(x-2)\left(x-6\right)}{(3x+1)\left(x-6\right)}[/tex]
[tex]=\frac{4(x-2)}{(3x+1)}[/tex]
Hence final answer is [tex]\frac{4(x-2)}{(3x+1)}[/tex]
