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.