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Question 423331: hi please help me with this problem of true or false . I'm a little rusty and need to see the steps thank you very much.
4 over (y+5) minus 8 over (y-5) = 8 over y^2 minus 25
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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