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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x + 1

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

Cancel the common factor:

x - 1

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

\frac{- 2 + 6}{2}

\frac{6 d ^{8}}{( 2 d ^{2} ) ^{3}}

(a + b c) (a - b c)

2^{- 3} \cdot 2

(3 y + 5)^{2}

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