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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

\frac{x ^{2}}{x ^{2}} = 1

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

Cancel

\frac{x}{x ^{2}} : \frac{1}{x}

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

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