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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Cancel

\frac{x ^{2}}{x ^{3}} : \frac{1}{x}

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

Cancel

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

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

(1 - y) ln (x + 1)

2 [(x + Δ x)^{2} + 1]

- \frac{7}{( x + 2 ) ( x - 5 )}

\frac{d ^{2}}{d t ^{2}} (x (t, α)) + ω^{2} (a cos (ω) t + α)

l im x \Rightarrow - 2 (x^{2} - x - 64 - 2 x)

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