y/(y^2 -64) + 2/(y-8) = 6/(y+8)?

y / (y² - 64) + 2 / (y-8) = 6 / (y+8)

y / [ (y - 8)*(y+8) ] + 2 / (y-8) - 6 / (y+8) = 0

y + 2 *(y+8) - 6 *(y-8) =0 {multiplied through by (y - 8)*(y+8) }

y + 2y + 16 - 6y +48 = 0

-3y + 64 = 0

y = 64/3

y/(y^2 - 64) + 2/(y - 8) = 6/(y + 8)
y/(y^2 - 64) + (2y + 16)/(y^2 - 64) = (6y - 48)/(y^2 - 64)
(y + 2y + 16 - 6y + 48)/(y^2 - 64) = 0
(-3y + 64)/(y^2 - 64) = 0
-3y + 64 = 0
-3y = -64
y = -64/-3
y = 64/3
y = 21 1/3

y/(y^2 -64) + 2/(y-8) = 6/(y+8)
y/(y-8)(y+8) + 2/(y-8) = 6/(y+8)

taking lcm, lcm is (y-8)(y+8)
so we get
y/(y-8)(y+8) + 2/(y-8) = 6/(y+8)
y + 2*(y+8) = 6*(y-8)
y + 2y+16 = 6y-48
3y+16=6y-48
16+48=6y-3y
64=3y
64/3=y
21.33=y

y / (y - 8)(y + 8) + 2 / (y - 8) = 6 / (y + 8)
y + 2 ( y + 8 ) = 6 (y - 8 )
y + 3y + 16 = 6y - 48
64 = 2y
y = 32