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

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

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expand (sqrt(x)-1+1/(sqrt(x)))^2

expand

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

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

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

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

Distribute parentheses

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

Simplify

x x + x (- 1) + x \frac{1}{x} - 1 \cdot x - 1 \cdot (- 1) - 1 \cdot \frac{1}{x} + \frac{1}{x} x + \frac{1}{x} (- 1) + \frac{1}{x} \cdot \frac{1}{x} : x - 2 x + 3 - \frac{2}{x} + \frac{1}{x}

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

(x - 6 + 5) (x - 6 - 5) (x - 4)

\frac{61 ( y ^{2} - 14 y + 49 )}{12}

\frac{2 ( 2 a - 1 )}{3 ( 10 a ^{2} - 5 )}

36 (e^{4} - e)

\frac{8}{( x + 8 ) ^{2}}

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