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

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

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

expand

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

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

Solution steps

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

(x + 1)^{3} = x^{3} + 3 x^{2} + 3 x + 1

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

Cancel

\frac{3 x}{x} : 3

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

a (- 1, - 3) b (5, 5) c (6, - 2)

(sec (θ) - csc (θ)) (cos (θ) + sin (θ))

(e^{x} - e^{- x})^{3}

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

(x + 33)^{2}