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3 over x minus 5 over x plus 2

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3 Answers

Anton, for this kind of problem you have to use parentheses, to avoid double reading!!

So, if second denominator is "x + 2" , then 3/x - 5/(x+2) ....
    3            5     
  ——  –  ————  =      
    x          x + 2

the LCD is  x(x + 2)

   3(x + 2)            5x   
 —————  –  —————  =
   x(x + 2)         x(x + 2)

  3x + 6 – 5x 
 —————— =
    x2 + 2x  

    6 – 2x  
 —————
   x2 + 2x 

3/x-5/x = -2/x  (Simplify like terms)  

-2/x + 2 =?  This is your answer.  You could multiply 2 by x/x and combine the numerators

(-2+2x)/x

It would be a different problem if this were an equation = 0.  But as you have it written, it is an expression.

3/x -5/x +2

Common denominator is x.

= -2/x + 2/1

Common denominator is x.

0/x.

Anything divided by, or into, 0... = 0 (zero)

Comments

-2/x + 2/1 = -2/x + 2x/x = (2x-2)/x, NOT 0!