What is expand ((x-2)(x+5))/(x^{3/2)} ?

The solution to expand ((x-2)(x+5))/(x^{3/2)} is x^{1/2}+3/(x^{1/2)}-(10)/(x^{3/2)}

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expand ((x-2)(x+5))/(x^{3/2)}

expand

\frac{( x - 2 ) ( x + 5 )}{x ^{\frac{3}{2}}}

x^{\frac{1}{2}} + \frac{3}{x ^{\frac{1}{2}}} - \frac{10}{x ^{\frac{3}{2}}}

Solution steps

\frac{( x - 2 ) ( x + 5 )}{x ^{\frac{3}{2}}}

Expand

(x - 2) (x + 5) : x^{2} + 3 x - 10

= \frac{x ^{2} + 3 x - 10}{x ^{\frac{3}{2}}}

Apply the fraction rule:

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

\frac{x ^{2} + 3 x - 10}{x ^{\frac{3}{2}}} = \frac{x ^{2}}{x ^{\frac{3}{2}}} + \frac{3 x}{x ^{\frac{3}{2}}} - \frac{10}{x ^{\frac{3}{2}}}

= \frac{x ^{2}}{x ^{\frac{3}{2}}} + \frac{3 x}{x ^{\frac{3}{2}}} - \frac{10}{x ^{\frac{3}{2}}}

Cancel

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

= x^{\frac{1}{2}} + \frac{3 x}{x ^{\frac{3}{2}}} - \frac{10}{x ^{\frac{3}{2}}}

Cancel

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

= x^{\frac{1}{2}} + \frac{3}{x ^{\frac{1}{2}}} - \frac{10}{x ^{\frac{3}{2}}}

\frac{9 x + 6}{( x + 3 ) \cdot x \cdot ( x - 4 )}

\frac{1}{2} sin (2 arcsin (\frac{1}{4} (x - 3)))

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

\frac{10}{4 - 3 x}

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

What is expand ((x-2)(x+5))/(x^{3/2)} ?
The solution to expand ((x-2)(x+5))/(x^{3/2)} is x^{1/2}+3/(x^{1/2)}-(10)/(x^{3/2)}