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

The solution to expand (x+1/x)^3 is (x^6+3x^4+3x^2+1)/(x^3)

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expand (x+1/x)^3

expand

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

\frac{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1}{x ^{3}}

Solution steps

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

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Simplify

x^{3} + 3 x^{2} \frac{1}{x} + 3 x (\frac{1}{x})^{2} + (\frac{1}{x})^{3} : \frac{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1}{x ^{3}}

= \frac{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1}{x ^{3}}

(4 + 2) (6 - 2)

(x^{2} + 2) (2 x - \frac{1}{x})^{4}

\frac{x ( x ^{2} + 4 )}{x ^{2} - 4}

(x - 6)^{2}

\frac{2 x ^{2} - 3}{( x ^{2} - 9 ) ( x ^{2} - 4 )}

What is expand (x+1/x)^3 ?
The solution to expand (x+1/x)^3 is (x^6+3x^4+3x^2+1)/(x^3)