When we can change the sign of denominatorSuppose z = − x 1 x 2 − x 3 , find − z.Which one is correct − z = x 1 x 2 − x 3 or − z = x 1 − x 2 + x 3

Question

When we can change the sign of denominatorSuppose   z  =            −              x        1                            x        2            −              x        3            , find   −  z.Which one is correct   −  z  =            x      1                      x        2            −              x        3                       or           −  z  =            x      1              −              x        2            +              x        3

Adolfo Rich · Accepted Answer

We have   z  =            −              x        1                            x        2            −              x        3              ,     −  z  =  (  −  1  )  ⋅            −              x        1                            x        2            −              x        3              −  z  =            x      1                      x        2            −              x        3              =            (                  −      1        1              )        ⋅            −              x        1                            x        2            −              x        3              =            (            1          −      1                  )                  −              x        1                            x        2            −              x        3              =            −              x        1                            x        3            −              x        2            Notice that in one of your proposed solutions above you would find the following:            x      1                      x        3            −              x        2              =            (      −      1      )      ⋅      (      −              x        1            )              (      −      1      )      ⋅      (              x        2            −              x        3            )        =            −              x        1                            x        2            −              x        3              =  zYou may only apply the negative factor to either the numerator or the denominator, but not both because they will negate eachother.

When we can change the sign of denominator Suppose z = −

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