What is (x^6-1)/(x^2-1) ?

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

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simplify (x^6-1)/(x^2-1)

simplify

\frac{x ^{6} - 1}{x ^{2} - 1}

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

Solution steps

\frac{x ^{6} - 1}{x ^{2} - 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 ^{2} - 1}

Factor

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

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

Cancel the common factor:

x + 1

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

Cancel the common factor:

x - 1

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

27 x^{9}

2 - 16

(3 x + y + 2)^{2}

n^{2} + 11 n + 10

\frac{15}{60}