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

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

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

expand

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

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

Solution steps

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

Expand

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

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

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

Cancel

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

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

(3 z - 2) (4 z + 3)

x^{x} (ln (x) + 1)

x (3 x - 10) - 31

\frac{1}{( 2 x + 1 ) ^{2}}

(x + \frac{3}{2})^{12}

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