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Differentiate w.r.t. x
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\frac{\left(x^{3}-3x^{2}+4x\right)\left(x-2\right)}{x-2}-\frac{5}{x-2}
To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3}-3x^{2}+4x times \frac{x-2}{x-2}.
\frac{\left(x^{3}-3x^{2}+4x\right)\left(x-2\right)-5}{x-2}
Since \frac{\left(x^{3}-3x^{2}+4x\right)\left(x-2\right)}{x-2} and \frac{5}{x-2} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{4}-2x^{3}-3x^{3}+6x^{2}+4x^{2}-8x-5}{x-2}
Do the multiplications in \left(x^{3}-3x^{2}+4x\right)\left(x-2\right)-5.
\frac{x^{4}-5x^{3}+10x^{2}-8x-5}{x-2}
Combine like terms in x^{4}-2x^{3}-3x^{3}+6x^{2}+4x^{2}-8x-5.