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