SOLUTION: Write in simplest form. 9-b^2/b^2-b-6 Thank you.

Question 29750: Write in simplest form.
9-b^2/b^2-b-6
Thank you.

Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
9-b^2/b^2-b-6 ----(1)
=[3^2-b^2]/(b-3)(b+2)
=(3+b)(3-b)/(b-3)(b+2)
[ using formula p^2-q^2 = (p+q)(p-q) and here p=3 and q=b in the nr
and factorisation in the dr(see note)]
=-(b-3)(b+3)/(b-3)(b+2)
[ since there is a factor (b-3) in the dr and we have (3-b) in the nr, so pull out a minus sign (that is take out (-1) and write (3-b)= -(b-3) ]
=-(b+3)/(b+2) (cancelling (b-3) )
Answer:9-b^2/b^2-b-6 =-(b+3)/(b+2)
Note: b^2-b-6 is a quadratic expression and
b^2-b-6 = b^2-3b+2b-6
(writing the middle term (-b) =-3b+2b so that (-3b)X(2b)=-6b^2 = (b^2)(-6)=product of the square term and the constant term)(which is the rule for factorisation)
= (b^2-3b)+(2b-6)
=b(b-3)+2(b-3)
=bp+2p where p=(b-3)
=p(b+2)
=(b-3)(b+2)
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