Question

What is the product in simplest form? State any restrictions on the variable. Please show your work.

Answer 1

You have the following expressions given in the problem above:

(y^2/y-3)(y^2-y-6/y^2+y)

By applying the exponents properties, you can simplify it, as it shown below:

(y^2/y-3)(y^2-y-6/y^2+y)
(y^4-y^3-6y^2)/(y^3+y^2-3y2-3y)
(y^4-y^3-6y^2)/(y^3-2y2-3y)

Then, you have:
y^2(y^2-y-6)/y(y^2-2y-3)
(y^2-y-6)/(y^2-2y-3)

The answer is: (y^2-y-6)/(y^2-2y-3)

Answer 2

The first term =
`(y^2)/(y-3)`
The second term =
`(y^2-y-6)/(y^2+y) = ((y-3)(y+2))/(y(y+1))` ⇒ factoring the numerator and denominator

multiplying the both terms:

`(y^2)/(y-3) * (y^2-y-6)/(y^2+y) = (y^2)/(y-3) * ((y-3)(y+2))/(y(y+1))`

=
`(y^2)/(y) * ((y-3)(y+2))/((y-3)(y+1)) = (y(y+2))/(y+1)`