What is (x^6-1)/(x^4-1) ?

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

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simplify (x^6-1)/(x^4-1)

simplify

\frac{x ^{6} - 1}{x ^{4} - 1}

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

Solution steps

\frac{x ^{6} - 1}{x ^{4} - 1}

Factor

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

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

Factor

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

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

Cancel the common factor:

x + 1

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

Cancel the common factor:

x - 1

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

(- x^{4})^{5}

(x^{2} + 10 x) - (- 4 x^{2} - x + 10)

2 y^{2} - 50

\frac{1}{x}

\frac{8 ^{3}}{4 ^{3}}

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