SOLUTION: Subtract and write in simplest form: 3/x^2+4x+3 subtracted by 1/x^2-9

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Question 81676: Subtract and write in simplest form: 3/x^2+4x+3 subtracted by 1/x^2-9
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure if I understand your question exactly, but does this look right?
3%2F%28x%5E2%2B4x%2B3%29-+1%2F%28x%5E2-9%29+

If this is what you meant, then remember that to subtract two fractions, you must have a common denominator! In order to do this, you must factor the two denominators to see what factors they have.
3%2F%28%28x%2B3%29%2A%28x%2B1%29%29-+1%2F%28%28x-3%29%2A%28x%2B3%29%29+

From this you can see that the LCD is +%28x%2B3%29%28x-3%29%28x%2B1%29+. Of course, you can write these factors in any order.

Now, you have to build each fraction so that it has the common denominator. You must decide what is missing from each denominator, and multiply the numerator and denominator by that missing factor. I have a lengthy explanation and a LOT of examples of this on my website.

%283%2A%28x-3%29-%28x%2B1%29%29%2F%28%28x%2B3%29%2A%28x-3%29%2A%28x%2B1%29%29+

Now, remember that these are TERMS in the numerator, and don't start "canceling" things out until you multiply out the numerator!
%283x-9-x-1%29%2F%28%28x%2B3%29%2A%28x-3%29%2A%28x%2B1%29%29+
%282x-10%29%2F%28%28x%2B3%29%2A%28x-3%29%2A%28x%2B1%29%29+
%282%28x-5%29%29%2F%28%28x%2B3%29%2A%28x-3%29%2A%28x%2B1%29%29+
Since the last answer does not reduce, the previous answer is also considered to be simplified completely and equally acceptable.

For more explanation like this, go to my website by clicking on my tutor name anywhere in algebra.com, and go to "Basic Algebra," then "Samples of Basic Algebra: One Step at a Time", then "Chapter 3", then "Section 3.04 Adding and Subtracting Fractions." See also my page called "Math in Living Color", then either "Basic or Intermediate Algebra", and look in Chapter 3 for Basic Algebra, or Chapter 2 for Intermediate Algebra. Let me know if you have trouble finding anything there!!

R^2 at SCC