Solve quadratic fractionI would like to simplify the fraction x 2 − 2 x x 2 + x − 6 I know from Mathematica that it should equal 3 3 x but how do I get there?

Question

Solve quadratic fractionI would like to simplify the fraction                    x        2            −      2      x                      x        2            +      x      −      6      I know from Mathematica that it should equal       3          3      x       but how do I get there?

humusen6p · Accepted Answer

The numerator factors as       x          2        −  2  x  =  x  (  x  −  2  )By the quadratic formula, the denominator has roots   2 and   −  3. So the denominator factors as       x          2        +  x  −  6  =  (  x  −  2  )  (  x  +  3  )Hence                     x                  2                    −      2      x                      x                  2                    +      x      −      6        =            x      (      x      −      2      )              (      x      −      2      )      (      x      +      3      )        =      x          x      +      3

crossoverman9b · Accepted Answer

x    2    +  x  −  6  =  (  x  −  2  )  (  x  +  3  )  →            x      (      x      −      2      )              (      x      +      3      )      (      x      −      2      )        =      x          x      +      3      , so your result is incorrect, as the next counterexample shows:  x  =  1  ;                    x        2            −      2      x                      x        2            +      x      −      6        =      1    4    ≠  1  =      3          3      x

Solve quadratic fraction I would like to simplify the fraction x

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