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:

$\frac{y (y + 2)}{(y + 1)} ,y \ne - 1$

EXPLANATION

The given expression is

$\frac{ {y}^{2} }{y - 3} \times \frac{ {y}^{2} - y - 6 }{ {y}^{2} + y }$

Split the middle term of the quadratic trinomial.

$\frac{ {y}^{2} }{y - 3} \times \frac{ {y}^{2} - 3y + 2y - 6 }{ {y}^{2} + y }$

Factor to obtain;

$\frac{ {y}^{2} }{y - 3} \times \frac{ y(y - 3)+ 2(y - 3)}{y(y + 1)}$

$\frac{ {y}^{2} }{y - 3} \times \frac{ (y - 3)(y + 2)}{y(y + 1)}$

Cancel out the common factors,

$= \frac{ y }{1} \times \frac{ (y + 2)}{(y + 1)}$

$= \frac{y (y + 2)}{(y + 1)} ,y \ne - 1$