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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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:
%284%29%2F%283-x%29+%2B+%282x%29%2F%28x-3%29
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(16949) About Me  (Show Source):
You can put this solution on YOUR website!
%284%29%2F%283-x%29+%2B+%282x%29%2F%28x-3%29
%284%29%2F%28-%28x-3%29%29+%2B+%282x%29%2F%28x-3%29
%28-4%29%2F%28x-3%29+%2B+%282x%29%2F%28x-3%29
LCD = (x-3)
..
%28-4%2B+2x%29%2F%28x-3%29
%282%28x-2%29%29%2F%28x-3%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
%284%29%2F%283-x%29+%2B+%282x%29%2F%28x-3%29
(x-3) = -(3-x)
--> 4/(3-x) - 2x/(3-x)


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Ok Whitney, here's how you would do this.
%284%2F%283-x%29%29%2B%282x%2F%28x-3%29%29 Take a look at the denominator in the first fraction.
3-x%29 let's factor out a -1 from this like so:-1%28-3%2Bx%29
Now we can switch the -3 and the x on the insides of the parentheses to get: -1%28x-3%29 and, as you probably know, we really don't need the 1 in front of the parentheses so we just write it as:-%28x-3%29 and now we can put it back in the fraction.
-%284%2F%28x-3%29%29%2B2x%2F%28x-3%29 Now we have our common denominator so we can just add the two numerators together to get:
%28-4%2B2x%29%2F%28x-3%29 and this can be written like:
%282x-4%29%2F%28x-3%29 In the numerator, we can factor out a 2 to get:
highlight%282%28x-2%29%2F%28%28x-3%29%29%29