7.2-7). Divide the following expressions. Be sure to reduce all answers to lowest terms.
6y^2+21y+9 12y^2+24y+9
____________ divide by _____________
y^2-16 2y^2-5y-12

Question

7.2-7). Divide the following expressions. Be sure to reduce all answers to lowest terms. 
    6y^2+21y+9                 12y^2+24y+9
    ____________ divide by  _____________
          y^2-16                      2y^2-5y-12

anonymous · Answer

each numerator and denominator can be factored

anonymous · Answer

6*y^2+21y+9=3*(2y+1)(y+3)
y^2-16=(y+4)(y-4)
12y^2+24y+9=3*(2y+3)(2y+1)
2y^2-5y-12=(2y+3)(y-4)
putting it all together we see that the 3 in front, (2y+3), (2y+1), and (y-4) all cancel.  We are left with 
(y+3)/(y+4)