If a b = x y , is x − a y − b = x y ?

Question

If       a    b    =      x    y  , is              x      −      a              y      −      b        =      x    y  ?

nifeonibonitozg · Accepted Answer

So by        a    b    =      x    y   we have   x  =  k  a,   y  =  k  b for some   k  ≠  0  ,  1. This gives            x      −      a              y      −      b        =            k      a      −      a              k      b      −      b        =            a      (      k      −      1      )              b      (      k      −      1      )        =      a    b    =      x    y    .

Riley Yates · Accepted Answer

a          b                                    =                  x          y                                              x          a                                    =                  y          b                                              x          a                −        1                            =                  y          b                −        1                                                  x            −            a                    a                                    =                              y            −            b                    b                                                          x            −            a                                y            −            b                                              =                  a          b                                                          x            −            a                                y            −            b                                              =                  x          y

If a b </mfrac> = x y </mfrac> , is x

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