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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

\frac{x ^{3}}{x ^{3}} = 1

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

Cancel

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

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

\frac{\partial}{\partial t} ((t) (v^{6} + uv w))

(x - \frac{1}{2} ln (x)) \cdot x

(4 - 4 + x)^{2}

- r P (1 - \frac{P}{k}) (1 - \frac{P}{T})

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

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