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

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

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

expand

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

Expand

x^{2} - 2 (x - 1) : x^{2} - 2 x + 2

= \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}}

A (1, 2) B (4, - 3)

\frac{( x - 4 ) ( 3 x - 1 )}{2}

a (- 3, - 1)

5 x (2 x - 3) (4 x + 9) (x - 3) (x + 3)

(2 m^{2 - m}) (7 m^{2 - 8 m + 5})

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