Question

What is the solution of -8 / 2 y - 8 equals 5 / y + 4 - 7 y + 8 / Y 2 - 16​

Answer 1

Answer:

The value of y is 6.

Step-by-step explanation:

The given equation is

$\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}$

It can be rewritten as

$\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}+\dfrac{7y+8}{y^2-4^2}$

$\dfrac{-4}{(y-4)}=\dfrac{5}{y+4}+\dfrac{7y+8}{(y+4)(y-4)}$

Multiply both sides by (y+4)(y-4).

$(y+4)(y-4)(\dfrac{-4}{(y-4)})=(y+4)(y-4)(\dfrac{5}{y+4})+(y+4)(y-4)(\dfrac{7y+8}{(y+4)(y-4)})$

$(y+4)(-4)=(y-4)(5)+7y+8$

$-4y-16=5y-20-(7y+8)$

$-4y-16=5y-20-7y-8$

$-4y-16=-2y-28$

$-4y+2y=-28+16$

$-2y=-12$

Divide both sides by -2.

$y=6$

Therefore, the value of y is 6.