What is expand ((x^3-1)(x^3-x^2+1))/(x^5+x+1) ?

The solution to expand ((x^3-1)(x^3-x^2+1))/(x^5+x+1) is x-1

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expand ((x^3-1)(x^3-x^2+1))/(x^5+x+1)

expand

\frac{( x ^{3} - 1 ) ( x ^{3} - x ^{2} + 1 )}{x ^{5} + x + 1}

x - 1

Solution steps

\frac{( x ^{3} - 1 ) ( x ^{3} - x ^{2} + 1 )}{x ^{5} + x + 1}

Expand

(x^{3} - 1) (x^{3} - x^{2} + 1) : x^{6} - x^{5} + x^{2} - 1

= \frac{x ^{6} - x ^{5} + x ^{2} - 1}{x ^{5} + x + 1}

Factor

x^{6} - x^{5} + x^{2} - 1 : (x - 1) (x^{5} + x + 1)

= \frac{( x - 1 ) ( x ^{5} + x + 1 )}{x ^{5} + x + 1}

Cancel the common factor:

x^{5} + x + 1

= x - 1

\frac{13 ( s + 2 )}{s ( s + 8 ) ( s + 1 )}

\frac{12.9282 ( 0.25 x ^{2} - 1 )}{2 + 0.44758 x ^{2}}

2 (sin (x) + x cos (x)) (2 cos (x) - x sin (x))

- 1 (- 5 x + 8 y = 5)

m (\frac{r ^{2}}{4} + \frac{l ^{2}}{3})

What is expand ((x^3-1)(x^3-x^2+1))/(x^5+x+1) ?
The solution to expand ((x^3-1)(x^3-x^2+1))/(x^5+x+1) is x-1