Ineed to simplify this problem in lowest terms

You should use a calculator this is very easy, you just add up the things in common and then then divide

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

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