Is it possible to manipulate: x 2 − 2 x + 1 such that the numerator has a lower power than the denominator?Is it possible to manipulate: x 2 − 2 x + 1 such that the numerator has a lower power than the denominator?For example: x + 3 x + 2 would be 1 + 1 x + 2

Question

Is it possible to manipulate:                     x        2            −      2              x      +      1       such that the numerator has a lower power than the denominator?Is it possible to manipulate:                     x        2            −      2              x      +      1       such that the numerator has a lower power than the denominator?For example:             x      +      3              x      +      2       would be   1  +      1          x      +      2

Leo Robinson · Accepted Answer

Hint                    x        2            −      2              x      +      1        =                    x        2            −      1              x      +      1        −      1          x      +      1

kituoti126 · Accepted Answer

This requires nothing smart: just do long division.                                                                                                              −                                                                              x                2                            +              0              x              −              2                                                          −                              x                2                            −                                                                    0                                                              x                                                                                                            −                    0                                                                                                          −              x              −              2                                                          x              +              1                                                          −              1                                                                                      x              +              1                                                          x              −              1                                          Or with an abbreviated scheme:                          1                    0                    −        2                            −        1                          −        1                    1                                  1                    −        1                    −        1            Both tell you that      x    2    −  2  =  (  x  −  1  )  (  x  +  1  )  −  1

Is it possible to manipulate: (x^2−2)/(x+1) such that the numerator has a lower power than the denominator? For example: (x+3)/(x+2) would be 1+1/(x+2).

Answered question

Answer & Explanation

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