# Math Help - basic Rational Expression simplifying help

1. ## basic Rational Expression simplifying help

ok so I have the following problem:

4x+2
-------- (fraction line, i thought this would be easier)
12x^2+14x+4

I can get pretty close to this but i get stuck along the way

i end up with:
2(2x+1)
-------------
3x(2x+1)+2(2x+1)

I dont know what to do, if I cancel out the 2x+1's im still left with a 2 as the numerator, if i cancel out the 2(2x+1) I feel like im breaking a rule because its part of addition (3x+2)

thanks for any help

2. Originally Posted by NecroWinter
ok so I have the following problem:

4x+2
-------- (fraction line, i thought this would be easier)
12x^2+14x+4

I can get pretty close to this but i get stuck along the way

i end up with:
2(2x+1)
-------------
3x(2x+1)+2(2x+1)

I dont know what to do, if I cancel out the 2x+1's im still left with a 2 as the numerator, if i cancel out the 2(2x+1) I feel like im breaking a rule because its part of addition (3x+2)

thanks for any help
note the denominator ... 3x(2x+1)+2(2x+1) = (2x+1)(3x+2)

$=\displaystyle\frac{2x+1}{6x^2+7x+2}$
$=\displaystyle\frac{2x+1}{(2x+1)(3x+2)}$