SOLUTION: how do you simplify this rational expression? (2/k-3)+ (4/k+3)= i was out sick for 3 days and i dont know how to do this.

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Question 166719: how do you simplify this rational expression?
(2/k-3)+ (4/k+3)=
i was out sick for 3 days and i dont know how to do this.
Found 2 solutions by nerdybill, MRperkins:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28k-3%29%2B+4%2F%28k%2B3%29
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Common denominator is:(k-3)(k+3)
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2%28k%2B3%29%2F%28%28k-3%29%28k%2B3%29%29%2B+4%28k-3%29%2F%28%28k-3%29%28k%2B3%29%29
%282%28k%2B3%29%2B+4%28k-3%29%29%2F%28%28k-3%29%28k%2B3%29%29
%282k%2B6%2B+4k-12%29%2F%28%28k-3%29%28k%2B3%29%29
%286k-6%29%2F%28%28k-3%29%28k%2B3%29%29
%286k-6%29%2F%28k%5E2%2B9%29

Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
Here is a quick lesson for you. First, think about fractions you can check for accuracy. Let's look at adding 2/3 and 3/4.
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We know that we can not add these two numbers as they are because they do not have the same denominator (the bottom number).
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So, we need to find a way to get the denominators to be the same. This is done by finding something called the least common multiple or LCM.
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The LCM will always contain the denominator of each term.
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The LCM of 2/3 and 3/4 is 12 so you multiply 2/3 by 4/4 and you get 8/12.
multiply 3/4 by 3/3 and you get 9/12. Now you can add 8/12 and 9/12 together to get 17/12.
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For your problem: the LCM is (k-3)*(k+3)
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Whenever both fractions have the LCM as the denominator then you will be able to add them together.
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In order to make the first term have (k-3)(k+3) you need to multiply the top and bottom (numerator and denominator) by (k+3). This is equivalent to multiplying the term by 1 because anything divided by itself is 1.
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So you have %282%28k%2B3%29%29%2F%28%28k-3%29%28k%2B3%29%29
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You need to do the same thing with the second fraction
%284%28k-3%29%29%2F%28%28k%2B3%29%28k-3%29%29
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now you can add the two fractions together

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notice on the sample problem that when adding 8 twelths and 9 twelths you get 17 twelths. The denominator stays the same when adding.
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So: can be written by adding the numerators over the same denominator like this:
%28%282%28k%2B3%29%29%2B%284%28k-3%29%29%29%2F%28%28k-3%29%28k%2B3%29%29
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remember (P)lease Excuse My Dear Aunt Sally for your order of operations
Parenthesis/Exponents
Multiply/Divide
Add/Subtract
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You are probably good once you get to this point so I will just show the final steps.
Distribute the 2 and the 4
%282k%2B6%2B4k-12%29%2F%28%28k-3%29%28k%2B3%29%29
combine like terms
%286k-6%29%2F%28%28k-3%29%28k%2B3%29%29
factor out a 6
%286%28k-1%29%29%2F%28%28k-3%29%28k%2B3%29%29
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If you have any questions, email me at justin.sheppard.tech@hotmail.com