How to compute t 2 t + 1 to the form 1 t + 1 + t − 1One of my attempts would look like below. t 2 t + 1 = t × t + 1 − 1 t + 1 = t − 1 t + 1 = t − 1 + 1 − 1 t + 1 + 1= − 2 t + 1 + 2Also, I put into t an arbitrary number in both equations and have gotten the same answer. The first number was 18785 to which both contained the answer 352876225 18786

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How to compute              t      2              t      +      1       to the form       1          t      +      1        +  t  −  1One of my attempts would look like below.             t      2              t      +      1      =            t      ×      t      +      1      −      1              t      +      1      =            t      −      1              t      +      1      =            t      −      1      +      1      −      1              t      +      1        +  1=            −      2              t      +      1        +  2Also, I put into t an arbitrary number in both equations and have gotten the same answer. The first number was 18785 to which both contained the answer       352876225    18786

razdiralem · Accepted Answer

we have            t      2              t      +      1        =                    t        2            −      1      +      1              t      +      1        =            (      t      −      1      )      (      t      +      1      )      +      1              t      +      1

rzfansubs87 · Accepted Answer

Several responses have you make the following factorization:            t      2              t      +      1        =            (      t      +      1      )      (      t      −      1      )      +      1              t      +      1      But in general, you can take a slightly more iterative approach:            t      2              t      +      1        =                    t        2            +      t      −      t              t      +      1        =            t      ⋅      (      t      +      1      )              t      +      1        −      t          t      +      1        =  t  −            (                  t      +      1      −      1              t      +      1                  )        =  t  −  1  +      1          t      +      1      You just need to consider which terms are required to turn the largest term in the numerator into a multiple of the denominator.

How to compute t 2 </msup> t + 1 </mr

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