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

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

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

expand

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

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

Solution steps

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

Expand

e^{x} (x - 1) : e^{x} x - e^{x}

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

Apply the fraction rule:

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

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

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

Cancel

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

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

- \frac{s + 3}{( s - 3 ) ( s + 2 ) ( s + 6 )}

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

\frac{s}{( s ^{2} + w ^{2} ) ( s ^{2} + 1 )}

\frac{i}{( x + i y ) ^{2}}

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