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\frac{x^{2}\left(x-2\right)}{x-4}
Divide x^{2} by \frac{x-4}{x-2} by multiplying x^{2} by the reciprocal of \frac{x-4}{x-2}.
\frac{x^{3}-2x^{2}}{x-4}
Use the distributive property to multiply x^{2} by x-2.
\frac{x^{2}\left(x-2\right)}{x-4}
Divide x^{2} by \frac{x-4}{x-2} by multiplying x^{2} by the reciprocal of \frac{x-4}{x-2}.
\frac{x^{3}-2x^{2}}{x-4}
Use the distributive property to multiply x^{2} by x-2.