SOLUTION: I need help with the following problems: 1) 2/x^2-x-12 - 6/x+4 = 2/x-3 2) x-1/3 + x+2/4 = 1/6 3) 5/3x - 1/9 = 1/x 4) 3/3x-2 = 4/2x+1 I need to solve these "Equations

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help with the following problems: 1) 2/x^2-x-12 - 6/x+4 = 2/x-3 2) x-1/3 + x+2/4 = 1/6 3) 5/3x - 1/9 = 1/x 4) 3/3x-2 = 4/2x+1 I need to solve these "Equations       Log On


   

Question 440679: I need help with the following problems:
1) 2/x^2-x-12 - 6/x+4 = 2/x-3
2) x-1/3 + x+2/4 = 1/6
3) 5/3x - 1/9 = 1/x
4) 3/3x-2 = 4/2x+1
I need to solve these "Equations with Rational Expressions" and i am having trouble figuring out how to find the LCD for some of them and others i just don't know how to go about solving them at all. Please help.
~ Thank you.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

If I am understqanding Your question(s) properly:

2) %28x-1%29%2F3+%2B+%28x%2B2%29%2F4+=+1%2F6   OR 

    4(x-1) + 3(x-2) = 2 |Multiplying thru with 12 so as all denominators = 1

        7x = 12

         x = 12/7

3) 5%2F%283x%29+-+1%2F9+=+1%2Fx  |Multiplying thru with 9x so as all denominators = 1

     3*5  - x = 9

        6 = x

4)+3%2F%283x-2%29+=+4%2F%282x%2B1%29   | Cross Multiplying 

       4(3x-2) = 3(2x+1)

          6x = 11

           x = 11/6



1)+2%2F%28x%5E2-x-12%29+-+6%2F%28x%2B4%29+=+2%2F%28x-3%29

  Check Your sign: should this be?

 +2%2F%28x%5E2%2Bx-12%29+-+6%2F%28x%2B4%29+=+2%2F%28x-3%29

then

    2 - 6(x-3) = 2(x+4)   |Multiplying thru with (x+4)(x-3):  %28x%5E2%2Bx-12%29

    2 - 6x + 18 = 2x+4

        16 = 8x

         x = 2