(x/x+y)+(x/x-y)

What you typed means this

 x         x
--- + y + --- - y
 x         x

I'm sure that's not what you meant as that is too easy:

1 + y + 1 - y 

which equals 2.

You didn't put in enough parentheses.  To type an expression all on one line,
you must begin every numerator and every denominator with a "(" and end it with
a "}"; otherwise you cannot tell where it starts and ends.  The only times you
don't need a pair of parentheses around a numerator or denominator is when it
contains only one number or one letter.

What I think you meant was this

  x       x
----- + -----
 x+y     x-y

which you should have typed on one line as:

x/(x+y) + x/(x-y)

==========================================

  x       x
----- + -----
 x+y     x-y

When the denominators have no common factor, as here, you may use
this rule:

     A     C     AD ± CB
    --- ± --- = ---------
     B     D        BD


  x       x      x(x-y) + x(x+y)
----- + ----- = ----------------- = (CAREFUL! NO CANCELLING BETWEEN
 x+y     x-y       (x+y)(x-y)        NUMERATOR AND DENOMINATOR ALLOWED HERE!)


      x² - xy + x² + xy
      -----------------
         (x+y)(x-y)


             2x²
        ------------
         (x+y)(x-y)


Edwin
AnlytcPhil@aol.com