What makes this answer unsimplified?Generally, what are the rules for simplifying answers?I had this question:Given f ( x ) = 1 x , evaluate f ( x ) − f ( a ) x − a .Why is the following a bad answer: 1 x − 1 a x − a The better answer is: − 1 x a Why is this? Is it generally just bad to leave fractions in either the numerator or denominator? So we should try to eliminate the fraction in the numerator by solving the equation first on the top by using a common denominator?

Question

What makes this answer unsimplified?Generally, what are the rules for simplifying answers?I had this question:Given   f  (  x  )  =      1    x  , evaluate             f      (      x      )      −      f      (      a      )              x      −      a      .Why is the following a bad answer:                    1        x            −              1        a                    x      −      a      The better answer is:            −      1              x      a      Why is this? Is it generally just bad to leave fractions in either the numerator or denominator? So we should try to eliminate the fraction in the numerator by solving the equation first on the top by using a common denominator?

Falpo359 · Accepted Answer

I like your bad answer better because                    1        x            −              1        a                    x      −      a        =  −      1          a      x      is true only if   x  ≠  a  .For   x  =  a the left hand side is undefined while the right hand side is defined unless   a  =  0

Arendrogfkl · Accepted Answer

&quot;Is it generally just bad to leave fractions in either the numerator or denominator?&quot;Yes, exactly. Intuitively, the simplified form of an expression is supposed to be the, well, simplest form. Exactly what constitutes &quot;fully simplified&quot; is subjective and can vary from person to person (is             2        2   simpler than       1          2      ?), but some things are pretty much constant across the board, one being that &quot;fractions inside fractions&quot; are to be avoided unless getting rid of them would add significant complexity to the expression.

Answered question

Answer & Explanation

New Questions in Pre-Algebra