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\frac{-\left(x+4\right)+x-2}{2}
Since -\frac{x+4}{2} and \frac{x-2}{2} have the same denominator, add them by adding their numerators.
\frac{-x-4+x-2}{2}
Do the multiplications in -\left(x+4\right)+x-2.
\frac{-6}{2}
Combine like terms in -x-4+x-2.
-3
Divide -6 by 2 to get -3.
\frac{-\left(x+4\right)+x-2}{2}
Factor out \frac{1}{2}.
-3
Simplify.