SOLUTION: This is subtracting a rational equation. I am not able to get it. Page 444 problem # 40 ( ISBN 0536269610) 5 30 ___ - ______ = 1 y-3

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Question 129175: This is subtracting a rational equation. I am not able to get it. Page 444 problem # 40 ( ISBN 0536269610)

5 30
___ - ______ = 1
y-3 y^2-9
or...
5/(y-3) - 30/y^2-9 = 1
Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for y:
%285%2F%28y-3%29%29-%2830%2F%28y%5E2-9%29%29+=+1 Factor the second denominator.
%285%2F%28y-3%29%29-%2830%2F%28%28y-3%29%28y%2B3%29%29%29+=+1 Multiply the first fraction by %28y%2B3%29%2F%28y%2B3%29 to get the fractions over a common denominator.
%285%28y%2B3%29-30%29%2F%28y-3%29%28y%2B3%29+=+1 Multiply both sides by %28y-3%29%28y%2B3%29
5%28y%2B3%29-30+=+%28y-3%29%28y%2B3%29 Perform the indicated multiplication on both sides.
5y%2B15-30+=+y%5E2-9 Simplify.
5y-15+=+y%5E2-9 Subtract 5y from both sides.
-15+=+y%5E2-5y-9 Add 15 to both sides.
y%5E2-5y%2B6+=+0 Factor this quadratic equation.
%28y-2%29%28y-3%29+=+0 Apply the zero product principle.
y-2+=+0 or y-3+=+0, therefore...
y+=+2 or y+=+3
CAUTION!!!
The original equation is:
5%2F%28y-3%29+-+30%2F%28y%5E2-9%29+=+1
If you substitute y = 3, you will get:
5%2F%283-3%29-30%2F%289-9%29 = %285%2F0%29-%2830%2F0%29...and, as you know, division by zero is undefined and thus not allowed.
So you have only one valid solution to this problem: y = 2