Answer
This equation has no solution.
Work Step by Step
$\dfrac{y}{2y+2}+\dfrac{2y-16}{4y+4}=\dfrac{2y-3}{y+1}$
Take out common factor $2$ from the denominator of the first fraction and common factor $4$ from the denominator of the second fraction:
$\dfrac{y}{2(y+1)}+\dfrac{2y-16}{4(y+1)}=\dfrac{2y-3}{y+1}$
Multiply the whole equation by $8(y+1)$
$8(y+1)\Big[\dfrac{y}{2(y+1)}+\dfrac{2y-16}{4(y+1)}=\dfrac{2y-3}{y+1}\Big]$
$4y+4y-32=16y-24$
Take all terms to the right side of the equation and simplify it by combining like terms:
$16y-24-4y-4y+32=0$
$8y+8=0$
Solve for $y$:
$8y=-8$
$y=-\dfrac{8}{8}$
$y=-1$
This is the solution found. Substituting $y=-1$ in the original equation makes all denominator $0$. Knowing that, we conclude that this equation has no solution.
