What is expand (e^x(x-3)^2)/((x-1)^3) ?

The solution to expand (e^x(x-3)^2)/((x-1)^3) is (e^xx^2-6e^xx+9e^x)/(x^3-3x^2+3x-1)

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expand (e^x(x-3)^2)/((x-1)^3)

expand

\frac{e ^{x} ( x - 3 ) ^{2}}{( x - 1 ) ^{3}}

\frac{e ^{x} x ^{2} - 6 e ^{x} x + 9 e ^{x}}{x ^{3} - 3 x ^{2} + 3 x - 1}

Solution steps

\frac{e ^{x} ( x - 3 ) ^{2}}{( x - 1 ) ^{3}}

(x - 1)^{3} = x^{3} - 3 x^{2} + 3 x - 1

= \frac{e ^{x} ( x - 3 ) ^{2}}{x ^{3} - 3 x ^{2} + 3 x - 1}

(x - 3)^{2} = x^{2} - 6 x + 9

= \frac{e ^{x} ( x ^{2} - 6 x + 9 )}{x ^{3} - 3 x ^{2} + 3 x - 1}

Expand

e^{x} (x^{2} - 6 x + 9) : e^{x} x^{2} - 6 e^{x} x + 9 e^{x}

= \frac{e ^{x} x ^{2} - 6 e ^{x} x + 9 e ^{x}}{x ^{3} - 3 x ^{2} + 3 x - 1}

\frac{( x + 5 ) ^{2} ( x - 5 ) ^{2}}{2 x}

\frac{2 ( - t ^{2} + 1 )}{( t ^{2} + 1 ) ^{2}}

\frac{2 ( 1 - 3 ^{\frac{2}{3}} ) ^{\frac{3}{2}} + 2}{3}

10 (- 2 e^{- 2 x} + 3 e^{- 3 x})

\frac{x ^{2} + 7 x + 11}{( x + 2 ) ( x + 1 ) ( x + 3 )}

What is expand (e^x(x-3)^2)/((x-1)^3) ?
The solution to expand (e^x(x-3)^2)/((x-1)^3) is (e^xx^2-6e^xx+9e^x)/(x^3-3x^2+3x-1)