Question

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

Answer 1

-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`