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How do you multiply #(3y-y^2)/(y^3-27) div y/(y^2+3y+9)#?

1 Answer

Jul 14, 2016

-1

Explanation:

=> #(3y-y^2)/(y^3-27) * (y^2+3y+9)/y#
=> #(y(3-y))/(y^3-3^3) * (y^2+3y+9)/y#

=>#(cancel(y)(3-y))/(y^3-3^3) * (y^2+3y+9)/cancel(y)#

#[a^3-b^3 = (a-b) (a^2+b^2+ab)#

=>#(3-y)/[(y-3) (y^2+3y+9)] * (y^2+3y+9)#
=>#(3-y)/[(y-3) cancel(y^2+3y+9)] * cancel(y^2+3y+9)#
=>#(3-y)/[(y-3)#
=>#(3-y)/-(3-y)#

=>#1/-1#
=> #-1#

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