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-\frac{2}{x+2}-\frac{2\left(x+2\right)}{x+2}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x+2}{x+2}.
\frac{-2-2\left(x+2\right)}{x+2}
Since -\frac{2}{x+2} and \frac{2\left(x+2\right)}{x+2} have the same denominator, subtract them by subtracting their numerators.
\frac{-2-2x-4}{x+2}
Do the multiplications in -2-2\left(x+2\right).
\frac{-6-2x}{x+2}
Combine like terms in -2-2x-4.