If a b = c + d e + f so a is equal to c + d?I have these question, a is always c+d and b is e+f ?.Thanks.

Question

If       a    b    =            c      +      d              e      +      f       so   a is equal to   c  +  d?I have these question, a is always c+d and b is e+f ?.Thanks.

Ryan Newman · Accepted Answer

NO.Here is an counterexample.      1    2    =            1      +      2              3      +      3      Obviously   1  ≠  1  +  2  =  3,   2  ≠  3  +  3  =  6

veirarer · Accepted Answer

There are plenty of easy counterexamples, of course.       1    1    =            2      +      3              2      +      3      , but   2  +  3  ≠  1. But what you suggest is true if both fractions are in reduced form - that is, if   a and   b are relatively prime and   c  +  d and   e  +  f are relatively prime.

If a b </mfrac> = c + d </mrow>

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