Basic Algebra/Rational Expressions and Equations/Adding and Subtracting When the Denominators are Different

Vocabulary

Lesson

If you have to add two rational fractions with different denominators, as the first step, you have to find the LCM:

  3   +   3
 x+1     x-1

  LCM = (x+1)(x-1)

Now divide the LCM by both denominators and multiply by their respectives numerators:

  (x+1)(x-1) / (x+1) = (x-1) . (3) = 3x-3
  (x+1)(x-1) / (x-1) = (x+1) . (3) = 3x+3

The sum of the two results would be the new nominator:

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

     6x
 (x+1)(x-1)

This is another example:

  6x   +   9x
 2x-6    x2-6x+9

We factorize both denominators and find the LCM

  2x-6 = 2(x-3)
  x2-6x+9 = (x-3)2
  LCM = 2(x-3)2

Now we divide and multiply:

  2(x-3)2 / 2(x-3) =
  2x2-12x+18 / 2x-6 = x-3
  (x-3) . 6x = 6x2-18x

  2(x-3)2 / (x-3)2 =
  2x2-12x+18 / x2-6x+9 = 2
  (2) . (9x) = 18x

We add the results to obtain the nominator; the denominator is the LCM:

  6x2-18x+18x = 
    2(x-3)2

   6x2
 2(x-3)2

We can factorize the nominator to simplify the result:

  2(3x2) =
  2(x-3)2

  3x2
 (x-3)2

Example Problems

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Last modified on 14 May 2010, at 19:29