Answer: 6
Step-by-step explanation:
[tex]\text{Difference:}\\\\.\quad \dfrac{6}{y-4}-\dfrac{y}{y+2}\\\\\\=\bigg(\dfrac{y+2}{y+2}\bigg)\dfrac{6}{y-4}-\dfrac{y}{y+2}\bigg(\dfrac{y-4}{y-4}\bigg)\\\\\\=\dfrac{6y+12}{(y+2)(y-4)}-\dfrac{y^2-4y}{(y+2)(y-4)}\\\\\\=\dfrac{6y+12-(y^2-4y)}{(y+2)(y-4)}\\\\\\=\dfrac{-y^2+10y+12}{(y+2)(y-4)}[/tex]
[tex]\text{Product:}\\\\.\quad \dfrac{(6)(y)}{(y-4)(y+2)}\\\\\\=\dfrac{6y}{(y-4)(y+2)}\\\\\\\text{Difference = Product:}\\\\\dfrac{-y^2+10y+12}{(y+2)(y-4)}=\dfrac{6y}{(y+2)(y-4)}\qquad Restriction: y\neq -2, 4\\\\\\\rightarrow -y^2+10y+12=6y\\\\\rightarrow 0=y^2-4y-12\\\\\rightarrow 0=(y-6)(y+2)\\\\\rightarrow 0=y-6\quad and\quad 0=y+2\\\\\rightarrow 6=y\qquad and\quad -2=y\\\\\text{Since y = -2 is a restricted value, it is not a valid solution}\\\text{So, y = 6}[/tex]
