What is the name for the mathematical property involving addition or subtraction of fractions over a common denominator?For any number x where x ∈ R and where x ≠ 0, what is the mathematical property which states that: 1 − x 2 x = 1 x − x 2 x

Question

What is the name for the mathematical property involving addition or subtraction of fractions over a common denominator?For any number   x where   x  ∈      R   and where   x  ≠  0, what is the mathematical property which states that:                    1        −                  x          2                    x        =            1      x        −                    x        2            x

1c2ru3x · Accepted Answer

Just the computation rules for fractions:            a      −      b        c    =            a      +      (      −      b      )        c                a      +      b        c    =      a    c    +      b    c                (      −      b      )        c    =  −      b    c  for   a  =  1,   b  =  −      x    2   and   c  =  x  ≠  0

Carlie Fernandez · Accepted Answer

In       R  , note that      x    y    =  x      y          −      1      , where       y          −      1       is defined as the number such that   y      y          −      1        =  1  =      y          −      1        y, and   x  −  y  =  x  +  (  −  y  ), where   −  y is defined as the number such that   y  +  (  −  y  )  =  0  =  (  −  y  )  +  y, and that   (  x  +  y  )  z  =  x  z  +  y  z (multiplication is left-distributive over addition)So, in any context in which   b has an additive inverse,   c has a multiplicative inverse, and multiplication is left-distributive over addition, the expression becomes:            a      −      b        c    =  (  a  +  (  −  b  )  )      c          −      1        =  a      c          −      1        +  (  −  b  )      c          −      1        =      a    c    −      b    c  Note that   0 cannot have a multiplicative inverse, so this is true only when   c  ≠  0

What is the name for the mathematical property involving addition or subtraction of fractions over a

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