SOLUTION: i need a little help subtracting this please! 3 over x^2+4x+3 minus 1 over x^2-9

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Question 76044: i need a little help subtracting this please!
3
over
x^2+4x+3
minus
1
over
x^2-9
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+%283%2F%28x%5E2%2B4x%2B3%29%29+-+%281%2F%28x%5E2-9%29%29+
Factor the denominators
+%283%2F%28x%2B1%29%28x%2B3%29%29+-+%281%2F%28x%2B3%29%28x-3%29%29+
Notice how the denominators each contain (x+3) .... but the one on the left is missing the (x-3) and the on the right is missing the (x+1). In order to have common denominators we must multiply the left side by (x-3)/(x-3) and the right by (x+1)/(x+1).

Now that we have like denominators, we can make it into one giant fraction.
+%283%28x-3%29-1%28x%2B1%29%29%2F%28x%2B1%29%28x%2B3%29%28x-3%29+
Distribute the 3 and the -1
+%283x-9-1x-1%29%2F%28x%2B1%29%28x%2B3%29%28x-3%29+
Combine like terms in the numerator
+%282x-10%29%2F%28x%2B1%29%28x%2B3%29%28x-3%29+
factor the numerator
+%282%28x-5%29%29%2F%28x%2B1%29%28x%2B3%29%28x-3%29+

Since you can not reduce the fraction by canceling like terms in the numerator and denominator, the problem is finished.