\(\dfrac{y}{y+3}-\dfrac{2y}{3-y}-\dfrac{3y^2+9}{y^2-9}=\dfrac{y\left(y-3\right)}{\left(y-3\right)\left(y+3\right)}+\dfrac{2y\left(y+3\right)}{\left(y-3\right)\left(y+3\right)}-\dfrac{3y^2+9}{\left(y-3\right)\left(y+3\right)}=\dfrac{y^2-3y+2y^2+6y-3y^2-9}{\left(y-3\right)\left(y+3\right)}=\dfrac{3y-9}{\left(y-3\right)\left(y+3\right)}=\dfrac{3\left(y-3\right)}{\left(y-3\right)\left(y+3\right)}=\dfrac{3}{y+3}\)
\(=\dfrac{y^2-3y+2y^2+6y-3y^2+9}{\left(y-3\right)\left(y+3\right)}=\dfrac{3y+9}{\left(y-3\right)\left(y+3\right)}=\dfrac{3}{y-3}\)
\(\dfrac{y\left(y-3\right)+2y\left(y+3\right)-3y^2+9}{\left(y+3\right)\left(y-3\right)}=\dfrac{y^2-3y+2y^2+6y-3y^2+9}{\left(y-3\right)\left(y+3\right)}=\dfrac{3y+9}{\left(y-3\right)\left(y+3\right)}=\dfrac{3\left(y+3\right)}{\left(y-3\right)\left(y+3\right)}=\dfrac{3}{y-3}\)
