SOLUTION: Hi, my name is Whitney and I have the answer to my math question, I just can't figure out how to get there. Here's the problem: {{{(4)/(3-x) + (2x)/(x-3)}}} I understand that

Question 336981: Hi, my name is Whitney and I have the answer to my math question, I just can't figure out how to get there. Here's the problem:

I understand that I need to find the least common denominator so I multiply (4)/(3-x) by (x-3)/(x-3) and (2x)/(x-3) by (3-x)/(3-x), after that, I am missing something. I end up with 2(5x-6-x^2)/(3-x)(x-3) and I don't see any way to factor it further. I am clearly wrong since the answer is suppose to be 2(x-2)/(x-3). Any help and explanation of what I'm not getting would be very appreciated.
Found 3 solutions by mananth, Alan3354, Earlsdon:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

LCD = (x-3)
..

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!

(x-3) = -(3-x)
--> 4/(3-x) - 2x/(3-x)

Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Ok Whitney, here's how you would do this.
Take a look at the denominator in the first fraction.
let's factor out a -1 from this like so:
Now we can switch the -3 and the x on the insides of the parentheses to get: and, as you probably know, we really don't need the 1 in front of the parentheses so we just write it as: and now we can put it back in the fraction.
Now we have our common denominator so we can just add the two numerators together to get:
and this can be written like:
In the numerator, we can factor out a 2 to get:

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