What is expand ((x-5)(x+1))/(x/(sqrt(x+1))) ?

The solution to expand ((x-5)(x+1))/(x/(sqrt(x+1))) is xsqrt(x+1)-4sqrt(x+1)-(5sqrt(x+1))/x

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expand ((x-5)(x+1))/(x/(sqrt(x+1)))

expand

\frac{( x - 5 ) ( x + 1 )}{\frac{x}{x + 1}}

x x + 1 - 4 x + 1 - \frac{5 x + 1}{x}

Solution steps

\frac{( x - 5 ) ( x + 1 )}{\frac{x}{x + 1}}

Apply the fraction rule:

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

= \frac{( x - 5 ) ( x + 1 ) x + 1}{x}

Expand

(x - 5) (x + 1) x + 1 : x^{2} x + 1 - 4 x x + 1 - 5 x + 1

= \frac{x ^{2} x + 1 - 4 x x + 1 - 5 x + 1}{x}

Apply the fraction rule:

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

\frac{x ^{2} x + 1 - 4 x x + 1 - 5 x + 1}{x} = \frac{x ^{2} x + 1}{x} - \frac{4 x x + 1}{x} - \frac{5 x + 1}{x}

= \frac{x ^{2} x + 1}{x} - \frac{4 x x + 1}{x} - \frac{5 x + 1}{x}

Cancel

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

= x x + 1 - \frac{4 x x + 1}{x} - \frac{5 x + 1}{x}

Cancel

\frac{4 x x + 1}{x} : 4 x + 1

= x x + 1 - 4 x + 1 - \frac{5 x + 1}{x}

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What is expand ((x-5)(x+1))/(x/(sqrt(x+1))) ?
The solution to expand ((x-5)(x+1))/(x/(sqrt(x+1))) is xsqrt(x+1)-4sqrt(x+1)-(5sqrt(x+1))/x