Question

Please help and explain the steps you took. Thank you.

What is the product in simplest form? State any restrictions on the variable. Please show your work. y^2/y-3 * y^2 - y-6/y^2 + y

Answer 1

$Domain:\\y-3\neq0\ \wedge\ y^2+y\neq0\\\\y\neq3\ \wedge\ y(y+1)\neq0\\\\y\neq3\ \wedge\ y\neq0\ \wedge\ y\neq-1$

$\dfrac{y^2}{y-3}\cdot\dfrac{y^2-y-6}{y^2+y}=\dfrac{y^2}{y-3}\cdot\dfrac{y^2-3y+2y-6}{y(y+1)}\\\\=\dfrac{y}{y-3}\cdot\dfrac{y(y-3)+2(y-3)}{y+1}=\dfrac{y}{y-3}\cdot\dfrac{(y-3)(y+2)}{y+1}\\\\=\dfrac{y}{1}\cdot\dfrac{y+2}{y+1}=\dfrac{y(y+2)}{1(y+1)}=\dfrac{y^2+2y}{y+1}$