Answer
This equation has no solution
Work Step by Step
$\dfrac{y}{2y+2}+\dfrac{2y-16}{4y+4}=\dfrac{y-3}{y+1}$
Factor the first and second rational expressions completely:
$\dfrac{y}{2(y+1)}+\dfrac{2(y-8)}{4(y+1)}=\dfrac{y-3}{y+1}$
Multiply the whole equation by $(2)(4)(y+1)$:
$(2)(4)(y+1)\Big[\dfrac{y}{2(y+1)}+\dfrac{2(y-8)}{4(y+1)}=\dfrac{y-3}{y+1}\Big]$
$4y+2(y-8)(2)=(y-3)(2)(4)$
$4y+4y-32=8y-24$
Take all terms to the left side of the equation:
$4y+4y-32-8y+24=0$
$-8\ne0$
This equation has no solution