SOLUTION: I can not figure this problem out...please help me. I am not getting any one of these answers....What am I doing wrong. Subtract. Write your answer in simplest form. y-2/y+3

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Question 47085: I can not figure this problem out...please help me. I am not getting any one of these answers....What am I doing wrong.
Subtract. Write your answer in simplest form.
y-2/y+3 - y/2y+6
Choices are: A) y^2+y-12/(y+3)(2y+6) B) y-2/y+3 C) y-4/2(y+3) D) 3y-4/2(y+3)
Found 2 solutions by mathchemprofessor, sae00:
Answer by mathchemprofessor(65) (Show Source):
You can put this solution on YOUR website!
y-2/y+3 - y/2y+6
LCM is (y+3)(2y+6)
On adding both of them, we get
((y-2)(2y+6)-y(y+3))/(y+3)(2y+6)
=2y^2+6y-4y-12-y^2-3y/(y+3)(2y+6)( expansion of the numerator)
=(y^2-y-12)/(y+3)(2y+6)(simplification of the numerator)
=(y-4)(y+3)/(y+3)(2y+6)(factoring the numerator)
=(y-4)/(2y+6) ( cancellation of the common term)
=(y-4)/2(y+3)

Answer by sae00(1) (Show Source):
You can put this solution on YOUR website!
the first answer seems long winded.
LCM is actually 2y+6
ie first term needs to be multiplied by 2/2 leading to
(2y-4-y)/(2y+6)=(y-4)/(2y+6) in one or two lines whic is same as previous answer