Question

1/(x+1) - 1/(x+2) = 1/2

Answer 1

Please include the instructions; I assume your job is to find the value of x.

1/(x+1) - 1/(x+2) = 1/2 would better be written as
   
     1            1            1
-------- - ------------ = ----
  x+1           x+2        2

Identify the LCD.  It is (x+1)(x+2)(2).  Mult. all 3 terms of the equation by this LCD:

2(x+2) - 2(x+1) = 2(x+1)(x+2)

We can factor out the 2 from all terms:

x+2 - x - 1 = x^2 + 3x + 2

Let's move all terms from the left to the right side:

 0              = x^2 + 3x + 2 - x - 2 + x + 1

Then x^2 + 3x + 1 = 0.  This is a quadratic with a=1, b=3 and c=1.

What is x?

       -3 plus or minus sqrt( 9-4(1)(1) )        -3 plus or minus sqrt(5)
x = --------------------------------------------- = ---------------------------------
                             2                                                    2

I rather expected to obtain an integer value for x.


Why don't you give this problem a try yourself?  Suggestion:  First mult. every term by 2.  This will give you:

   2          2
------- - ------- = 1   and this may be slightly easier to work with.  Please
 x+1      x+2          give it a try:  try to find x that satisfies this equation. 
                              Important:  note that x cannot equal either -1 or -2.