Algebraic fractions: addition I have very elementary question about adding algebraic fractions. Now, I know the following: a c + b d = d a + c b d c My question is however, how given this expression: ( 2 n + 1 ) n ( n + 1 ) 2 + ( 2 n + 1 ) n ( n + 1 ) 6 One arrives at: ( 2 n + 1 ) n ( n + 1 ) 3 Trying to work out the solution, I arrive at a very large equation divided by 12...

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Algebraic fractions: addition I have very elementary question about adding algebraic fractions. Now, I know the following:      a    c    +      b    d    =            d      a      +      c      b              d      c      My question is however, how given this expression:            (      2      n      +      1      )            n      (      n      +      1      )        2    +            (      2      n      +      1      )            n      (      n      +      1      )        6  One arrives at:            (      2      n      +      1      )            n      (      n      +      1      )        3  Trying to work out the solution, I arrive at a very large equation divided by 12...

Arabella Alvarez · Accepted Answer

(      2      n      +      1      )      n      (      n      +      1      )        2    +            (      2      n      +      1      )      n      (      n      +      1      )        6    =  (  2  n  +  1  )  n  (  n  +  1  )  ⋅      (          1      2        +          1      6        )    =            2      (      2      n      +      1      )      n      (      n      +      1      )        3    .

Despiniosnt · Accepted Answer

One should not arrive at that value, as it is not true. Notice that the numerators are the same. This is essentially            (      2      n      +      1      )      n      (      n      +      1      )        2    +            (      2      n      +      1      )      n      (      n      +      1      )        6    =  (  2  n  +  1  )  n  (  n  +  1  )      (          1      2        +          1      6        )    .Now, it is easy to show that        1    2    +      1    6    =      2    3  , so you should get            2      (      2      n      +      1      )      n      (      n      +      1      )        3    .

Algebraic fractions: addition I have very elementary question about adding algebraic fractions. No

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