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\frac{2}{x+3}-\frac{2\left(x+3\right)}{x+3}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x+3}{x+3}.
\frac{2-2\left(x+3\right)}{x+3}
Since \frac{2}{x+3} and \frac{2\left(x+3\right)}{x+3} have the same denominator, subtract them by subtracting their numerators.
\frac{2-2x-6}{x+3}
Do the multiplications in 2-2\left(x+3\right).
\frac{-4-2x}{x+3}
Combine like terms in 2-2x-6.