SOLUTION: I previously asked this and no one answered. Please help!! Add. Express answer in simplest form 4x/x^2-18x+72 + 4/x-6

Question 38591: I previously asked this and no one answered. Please help!!
Add. Express answer in simplest form
4x/x^2-18x+72 + 4/x-6
Found 2 solutions by fractalier, rapaljer:
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
From
4x/)x^2-18x+72) + 4/(x-6)
we factor the denominator of the first fraction and get
4x/(x-12)(x-6) + 4/(x-6)
Notice that if we multiply the second fractaion by (x-12)/(x-12), we will have common denominators...so
4x/(x-12)(x-6) + 4(x-12)/(x-6)(x-12) =
(4x + 4x - 48) / (x-6)(x-12) =
8x-48 / (x-6)(x-12) =
8(x-6) / (x-6)(x-12) =
8 / (x-12)
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!

Notice that the first denominator probably factors, and looking at the second denominator you might suspect that one of the factors is (x-6). Indeed it is!! The first denominator factors into (x-6)(x-12). Isn't that a coincidence???

In order to get a common denominator, you need to multiply the numerator and denominator of the second fraction by (x-12). It should now look like this:

Now, the denominator of the answer is the LCD, which is (x-6)(x-12).
To get the numerator, just add the numerators of the two fractions:

This factors into

and the fraction reduces by dividing out the (x-6) factors:

Nice problem!! I'm sorry no one answered it earlier for you! I have not had much time lately!

R^2 at SCC

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