What is (x+1/x)(x-1/x+1) ?

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

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simplify (x+1/x)(x-1/x+1)

simplify

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

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

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Apply exponent rule:

aa = a^{2}

xx = x^{2}

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

\frac{d}{d x} ((z) (x^{3} + y^{3} + z^{3} + 6 x y z - 2))

(x + 3) (x + 2)

\frac{( - 3 + 9 t ) 3}{2}

(1 + sec (y))^{2}

\frac{5 e ^{2 x} ( 2 x - 3 )}{x ^{4}}

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