Question

What is the product in simplest form? State any restrictions on the variable. y2/y-3 x y^2-y-6/y^2+1y

Answer 1

ANSWER

The product in simplest form is:


`(y (y + 2))/((y + 1)) ,y \\e - 1`

Step-by-step explanation

The given expression is


`\frac{ {y}^(2) }{y - 3} * \frac{ {y}^(2) - y - 6 }{ {y}^(2) + y }`

Split the middle term of the quadratic trinomial.


`\frac{ {y}^(2) }{y - 3} * \frac{ {y}^(2) - 3y + 2y - 6 }{ {y}^(2) + y }`

Factor to obtain;


`\frac{ {y}^(2) }{y - 3} * ( y(y - 3)+ 2(y - 3))/(y(y + 1))`


`\frac{ {y}^(2) }{y - 3} * ( (y - 3)(y + 2))/(y(y + 1))`

Cancel out the common factors,


`= ( y )/(1) * ( (y + 2))/((y + 1))`


`= (y (y + 2))/((y + 1)) ,y \\e - 1`