What is expand (((x^3-2x)^2-1))/(x^2-1) ?

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

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expand (((x^3-2x)^2-1))/(x^2-1)

expand

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

x^{4} - 3 x^{2} + 1

Solution steps

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

Expand

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

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

Factor

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

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

Factor

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

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

Cancel

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

= x^{4} - 3 x^{2} + 1

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

\frac{( x - 2 ) x ( x ^{2} + 44 )}{( x + 8 ) ( x + 4 )}

(2 x - 2 y) d x + (y - 1) d y

\frac{2}{( s - 3 ) ( s ^{2} + 4 )}

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

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