Question 423331
you either want to make all the denominators the same or you want to remove the denominator from the equation.


i find that, in this case, removing the denominator entirely is the way to go.


note that y^2 - 25 is equal to (y-5) * (y+5)


if you multiply both sides of this equation by (y-5) * (y+5), then you will get:


4 * (y-5) - 8 * (y+5) = 8


remove parentheses to get:


4*y - 20 - 8*y - 40 = 8


combine like terms to get:


-4*y - 60 = 8


add 4*y to both sides of the equation and subtract 8 from both sides of the equation to get:


-60 - 8 = 4*y


simplify to get:


-68 = 4*y


solve for y to get:


y = -17


plug the value of y into your original equation to confirm this answer is good.


your original equation is:


4/(y+5) - 8/(y-5) = 8/y^2-25)


substitute -17 for y to get:


4/(-17+5) - 8/(-17-5) = 8/((-17)^2 - 25))


simplify to get:


4/(-12) - 8/(-22) = 8/(264)


multiply both sides of this equation by 264 to get:


4*(-22) - 8*(-12) = 8


simplify to get:


-88 + 96 = 8


combine like terms to get:


8 = 8 confirming the value of y = -17 is good.