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

The solution to expand (e^x(x^2-2x+2))/(x^3) is (e^x)/x-(2e^x)/(x^2)+(2e^x)/(x^3)

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

expand

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

\frac{e ^{x}}{x} - \frac{2 e ^{x}}{x ^{2}} + \frac{2 e ^{x}}{x ^{3}}

Solution steps

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

Expand

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

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

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

Cancel

\frac{e ^{x} x ^{2}}{x ^{3}} : \frac{e ^{x}}{x}

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

Cancel

\frac{2 e ^{x} x}{x ^{3}} : \frac{2 e ^{x}}{x ^{2}}

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

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

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

\frac{d}{d y} ((z) (z^{3} - x y + y z + y^{3} - 2))

\frac{1 + sin ( x ) ( 1 - sin ( x ) )}{cos ( x )}

(x^{2} + 2 x y - y^{2}) d x + (y^{2} + 2 x y - x^{2}) d y

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