What is (8/(8-x^3)+x/(x-2)-1)*(x/(x+2)-(x+2)/x) ?

The solution to (8/(8-x^3)+x/(x-2)-1)*(x/(x+2)-(x+2)/x) is (2(-4x-4))/((x-2)(x^2+2x+4))

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simplify (8/(8-x^3)+x/(x-2)-1)*(x/(x+2)-(x+2)/x)

simplify

(\frac{8}{8 - x ^{3}} + \frac{x}{x - 2} - 1) \cdot (\frac{x}{x + 2} - \frac{x + 2}{x})

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

Solution steps

(\frac{8}{8 - x ^{3}} + \frac{x}{x - 2} - 1) (\frac{x}{x + 2} - \frac{x + 2}{x})

Join

\frac{8}{8 - x ^{3}} + \frac{x}{x - 2} - 1 : \frac{2 x ^{2} + 4 x}{( x - 2 ) ( x ^{2} + 2 x + 4 )}

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

Apply the fraction rule:

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

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

Simplify

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

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

(3 x^{2} y^{4} - 3 y z^{2}) (- 3 x^{2} y^{4} - 3 y z^{2})

2744

(5 y - 7) (- y)

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

What is (8/(8-x^3)+x/(x-2)-1)*(x/(x+2)-(x+2)/x) ?
The solution to (8/(8-x^3)+x/(x-2)-1)*(x/(x+2)-(x+2)/x) is (2(-4x-4))/((x-2)(x^2+2x+4))