SOLUTION: {{{(y-2)/(y+3)-y/(2y+6)}}}=????? I need some help with this one. I came up with y^2+5y-12. Is this correct???

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {{{(y-2)/(y+3)-y/(2y+6)}}}=????? I need some help with this one. I came up with y^2+5y-12. Is this correct???      Log On


   

Question 69607: %28y-2%29%2F%28y%2B3%29-y%2F%282y%2B6%29=?????
I need some help with this one. I came up with y^2+5y-12. Is this correct???
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%28y-2%29%2F%28y%2B3%29-y%2F%282y%2B6%29=????? 
I need some help with this one.
I came up with y%5E2%2B5y-12. 
Is this correct???

-----------------------------

No, I'm afraid not.

%28y-2%29%2F%28y%2B3%29-y%2F%282y%2B6%29

Factor the second denominator:

%28y-2%29%2F%28y%2B3%29-y%2F%282%28y%2B3%29%29

The LCD is 2%28y%2B3%29

The second fraction already has this LCD
for its denominator.  To make the first
fraction also have the LCD for its
denominator, multiply top and bottom by 2.

+%282%28y-2%29%29%2F%282%28y%2B3%29%29-y%2F%282%28y%2B3%29%29+

Remove parentheses in the top but NOT
the bottom.

+%282y-4%29%2F%282%28y%2B3%29%29-y%2F%282%28y%2B3%29%29+

Combine numerators over the LCD, all
as just one fraction:

+%282y-4-y%29%2F%282%28y%2B3%29%29+


simplify

+%28y-4%29%2F%282%28y%2B3%29%29+

Edwin