SOLUTION: How can I simplify this rational expression? 2x^2 +11x+5/3x^2-5x+2 I've tried to factor it but after I use the "diamond method" but I can't seem to come up with two separate f

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Question 723479: How can I simplify this rational expression?
2x^2 +11x+5/3x^2-5x+2
I've tried to factor it but after I use the "diamond method" but I can't seem to come up with two separate factors, meaning factors that look a little like: (x+__)(x-__)
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
This is the first I've ever heard of the "diamond method". I'll try to explain how it will factor the numerator and denominator.


  1. a*c = 10 so a 10 goes in the top box
  2. b is 11 so an 11 goes in the bottom box
  3. The factors of the 10 in the top box that add up to the 11 in the bottom box are 10 and 1. So a 10 and a 1 go in the left and right boxes.
  4. Next we make fractions in the left and right boxes. The numbers that are there, 10 and 1, go into the denominators of these fractions. The numerators will be a*x. Since the a is 2 in this problem, the numerators will be "2x". So the left and right boxes now have "2x/10" and "2x/1" in them.
  5. Reduce but don't eliminate the fractions in the left and right boxes. The "2x/10" fraction will reduce to "x/5". Normally we would simplify "2x/1" to just "2x" but we do not want to eliminate the fraction so we will leave it as "2x/1".
  6. The factors are formed from the fractions in the left and right boxes. The factors will be of the form: (numerator + denominator). So "x/5" becomes the factor (x+5) and the "2x/1" becomes the factor (2x+1)
So

Repeating this with :
  1. Top box: 6
  2. Bottom box: -5
  3. Left and right box: -2 and -3 (Don't forget the negative factors of positive numbers!)
  4. Left and right boxes: 3x/-2 and 3x/-3
  5. Left and right boxes: 3x/-2 and x/-1
  6. Factors: (3x + (-2)) and (x + (-1))
So or (3x-2)(x-1)

So . Since there are no common factors between the numerator and denominator, this fraction will not reduce.
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