Answer:
The value of y is 6.
Step-by-step explanation:
The given equation is
[tex]\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}[/tex]
It can be rewritten as
[tex]\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}+\dfrac{7y+8}{y^2-4^2}[/tex]
[tex]\dfrac{-4}{(y-4)}=\dfrac{5}{y+4}+\dfrac{7y+8}{(y+4)(y-4)}[/tex]
Multiply both sides by (y+4)(y-4).
[tex](y+4)(y-4)(\dfrac{-4}{(y-4)})=(y+4)(y-4)(\dfrac{5}{y+4})+(y+4)(y-4)(\dfrac{7y+8}{(y+4)(y-4)})[/tex]
[tex](y+4)(-4)=(y-4)(5)+7y+8[/tex]
[tex]-4y-16=5y-20-(7y+8)[/tex]
[tex]-4y-16=5y-20-7y-8[/tex]
[tex]-4y-16=-2y-28[/tex]
[tex]-4y+2y=-28+16[/tex]
[tex]-2y=-12[/tex]
Divide both sides by -2.
[tex]y=6[/tex]
Therefore, the value of y is 6.
