SOLUTION: I am having trouble. I am in college algebra and we are having to simplify rational expressions. The equation I have is a fraction: 5/(a-3)-2/(a^2-9) I do not know how to get

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Question 467456: I am having trouble. I am in college algebra and we are having to simplify rational expressions. The equation I have is a fraction:
5/(a-3)-2/(a^2-9) I do not know how to get to the answer. I have to show my work, but I don't know what steps to take and my book is so confusing. I don't want to cheat, I just genuinely want to understand, but am stuck. Please help!!!
Found 2 solutions by stanbon, algebrahouse.com:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
5/(a-3)-2/(a^2-9)
----
Factor:
[5/(a-3)] - [2/(a-3)(a+3)]
----
Least common denominator: (a-3)(a+3)
----
Rewrite each fraction with the lcd as its denominator:
---
= [5(a+3)/lcd] - [2/lcd]
-----
Combine the numerators over the common denominator:
= [5a+15-2]/lcd
-----------------------
simplify:
---
= [5a+13]/[(a-3)(a+3)]
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cheers,
stan H.
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Answer by algebrahouse.com(1659) (Show Source):
You can put this solution on YOUR website!
When adding and subtracting fractions, you have to get a common denominator.
To do that, all of the denominators need to be completely factored:

5/(a - 3) - 2/(a� - 9)
= 5/(a - 3) - 2/(a + 3)(a - 3) {factored a� - 9 into two binomials}
= 5(a + 3)/(a + 3)(a - 3) - 2/(a + 3)(a - 3) {got common denominator of (a + 3)(a - 3)}

5(a + 3) - 2
------------- {combined numerators over common denominator}
(a + 3)(a - 3)

5a + 15 - 2
-------------- {used distributive property in numerator}
(a + 3)(a - 3)

5a + 13
-------------- {combined like terms in numerator}
(a + 3)(a - 3)

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