SOLUTION: I am so lost. What am I overlooking? The problem is : (1-3y / y) / ((9/y^2)-1)

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Question 87996: I am so lost. What am I overlooking? The problem is :
(1-3y / y) / ((9/y^2)-1)
Found 2 solutions by Earlsdon, rapaljer:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
%28%28%281-3y%29%29%2Fy%29%2F%28%289%2Fy%5E2%29-1%29 First, simplify the denominator.
%28%281-3y%29%2Fy%29%2F%28%289-y%5E2%29%2Fy%5E2%29 Invert the denomiator and multiply.
%28%281-3y%29%2Fy%29%28y%5E2%2F%289-y%5E2%29%29 Cancel a y in the top and bottom.
y%281-3y%29%2F%289-y%5E2%29%29
%28y-3y%5E2%29%2F%289-y%5E2%29

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
This must be a complex fraction. Is this what you mean??
%28%281-3y%29+%2F+y%29+%2F+%28%289%2Fy%5E2%29-1%29
If so, I have an extensive lesson plan in algebra.com and also on my own website. You can see MY problems which are solved in LIVING COLOR at my website. Click on my tutor name "rapaljer" and look for "MATH IN LIVING COLOR", then go to COLLEGE ALGEBRA, Chapter 1, "Complex Fractions".

Before I continue, I have tried to work this out, and it doesn't come out like complex fractions usually do. I think you copied it wrong, and I'm going to fix it like I think it might have been written. If I am wrong, then resubmit the problem or send me an Email.

I think the problem works out nicely if you write it this way:
%281-3%2Fy%29+%2F+%28%289%2Fy%5E2%29-1%29

There are two methods commonly used to simplify complex fractions. I recommend that you begin by "unstacking" the problem.

%281-3%2Fy%29+%2F+%28%289%2Fy%5E2%29-1%29= +1-3%2Fy+ divided by +%289%2F%28y%5E2%29%29+-1+
Get a common denominator of y for the first fractions, and y%5E2 for the second fractions .
+%281%2F1%29-3%2Fy+ divided by +%289%2F%28y%5E2%29%29+-%281%2F1%29+
+%281%2F1%29%2A%28y%2Fy%29-3%2Fy+ divided by +%289%2F%28y%5E2%29%29+-%281%2F1%29%2A%28%28y%5E2%29%2F%28y%5E2%29%29+
+%28y-3%29%2Fy+ divided by +%289-y%5E2%29%2F%28y%5E2%29+

Now, invert the second fraction and multiply.
+%28%28y-3%29%2Fy%29%2A%28%28y%5E2%29%2F%289-y%5E2%29%29
Factor the second denominator as the difference of two squares:
%28%28y-3%29%2Fy%29%2A%28%28y%5E2%29%2F%28%283-y%29%283%2By%29%29%29

The factor of y in the first denominator divides into the y^2 in the second numerator leaving a y factor in the numerator.

The factor of (y-3) in the first numerator divides with the factor of (3-y) in the second denominator leaving a factor of -1, which you can put in either the numerator or the denominator. Put it in the numerator. This is what is left, the final answer:
%28-y%29%2F%283%2By%29+ or -y%2F%28y%2B3%29+

R^2 Retired from SCC