Okay I'm pretty sure this is right but not entirely...
First you would factor both the numerator and the denominator.
3x³+13x²+4x (You can factor out an x, and simplify it...)
3x³+13x²+4x= x(3x+1)(x+4)
3x³-2x²-x (You can factor out an x and simplify it...)
3x³-2x²-x= x(3x+1)(x-1)
The new fraction is
x(3x+1)(x+4)/x(3x+1)(x-1)
You can cancel out the x's and the (3x+1)'s,
So your new fraction is
x+4/x-1
