SOLUTION: Directions say to find the LCD(least common denominator): 1divided by 6y, 3xdivided by 4y+12 heres the work i have done: 1 divided by (y+2)(y+3), 3x divided by 4(y+3) thanks

Directions say to find the LCD(least common denominator): 
1 divided by 6y, 3xdivided by 4y+12
heres the work i have done:
1 divided by (y+2)(y+3), 3x divided by 4(y+3).

I don't know where you got "(y+2)(y+3)" from what you give here:

 1       3x
————, ————————
 6y    4y+12

Let's start over.  You did right by factoring 4y+12 as 4(y+3)


 1       3x
————, ————————
 6y    4(y+3)

The prime factorization of 6y is 2·3·y

The prime factorization of 4(y+3) is 2·2·(y+3)

Each of the prime factors 2, 3, y, and (y+3) must occur in
the LCD as many times as it occurs in any one of the two factors

2 occurs one time in the first denominator and two times in the second.
That's at most two times. So the LCD must contain the factor 2 two times.

So far the LCD = 2·2

3 occurs one time in the first denominator and NO times in the second.
That's at most one time. So the LCD must contain the factor 3 one time.

So far the LCD = 2·2·3

y occurs one time in the first denominator and NO times in the second.
That's at most one time. So the LCD must contain the factor y ONE time.

So far the LCD = 2·2·3·y

Finally, (y+3) occurs NO times in the first denominator and one time 
in the second. That's at most one time.  So the LCD must contain the 
factor (y+3) one time.

So the final LCD = 2·2·3·y·(y+3) or 12y(y+3)

Edwin
AnlytcPhil@aol.com