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\frac{2x^{2}}{x-4}+\frac{-2x\left(x-4\right)}{x-4}
To add or subtract expressions, expand them to make their denominators the same. Multiply -2x times \frac{x-4}{x-4}.
\frac{2x^{2}-2x\left(x-4\right)}{x-4}
Since \frac{2x^{2}}{x-4} and \frac{-2x\left(x-4\right)}{x-4} have the same denominator, add them by adding their numerators.
\frac{2x^{2}-2x^{2}+8x}{x-4}
Do the multiplications in 2x^{2}-2x\left(x-4\right).
\frac{8x}{x-4}
Combine like terms in 2x^{2}-2x^{2}+8x.