Question is simplify the following expression
1 _ 1
x+2 x+4
That's not valid! x + 2 can be thought of as a single number that is dividing into 1, and if you are multiplying the 2 by 2, you have to multiply the x by 2 as well.
$\displaystyle 2(x + 2) = x2 + 4$
Maybe if you substituted x + 2 and x + 4 as a single variable, you will see how your method was wrong and you will also see the correct way to solve this problem:
$\displaystyle j = x + 2$
$\displaystyle v = x + 4$
$\displaystyle \frac{1}{j} - \frac{1}{v}$
Simplify this just like you did the example, and at the end, put in the true values of j and v back in.