SOLUTION: I submitted this problem yesterday. I recd a response for one of the problems but I'm not sure which one the answer was for and I'm not sure how the answer came to be. I asked the

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Question 115605: I submitted this problem yesterday. I recd a response for one of the problems but I'm not sure which one the answer was for and I'm not sure how the answer came to be. I asked the tutor for clarification, but I didn't get a response. Can you please help me with these two again with a bit more detail.
2 OVER 5w + 10 MINUS 3 OVER 2w - 4

3 OVER x squared + 4x + 3 MINUS 1 OVER x squared - 9
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
2 OVER 5w + 10 MINUS 3 OVER 2w - 4
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2/(5w+10) - 3/(2w-4)
= 2/(5(w+2)) - 3/(2(w-2)]
Least common denominator: 2*5(w+2)(w-2)
Write each fraction with the lcd as its denominator:
=[2*2(w-2)]/lcd - [3*5(w+2)]/lcd
=Combine the fractions:
[4(w-2)-15(w+2)]/lcd
[-7w-38]/lcd
= [-7w-38]/[10(w^2-4)]
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3 OVER x squared + 4x + 3 MINUS 1 OVER x squared - 9
3/(x^2+4x+3) - 1/(x^2-9)
= 3/[(x+3)(x+1)] - 1/(x-3)(x+3)
lcd = (x+1)(x+3)(x-3)
Rewrite each fraction over the lcd
= [3(x-3) - (x+1)]/lcd
Combine the fractions:
= [3x-9 - x-1]/lcd
= [2x-8]/lcd
= [2(x-4)]/[(x+1)(x^2-9)]
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Cheers,
Stan H.