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

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

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expand ((x+1)^3)/(x^{3/2)}

expand

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

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

Solution steps

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

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

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

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

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

Cancel

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

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

Cancel

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

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

Cancel

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

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

4 (sin (4) cos (4) + x cos (2 4^{\circ}))

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

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4 e (3 e - 5) - 2 e (e - 7)

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