What is (x^2-1)/(x^4-1) ?

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

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simplify (x^2-1)/(x^4-1)

simplify

\frac{x ^{2} - 1}{x ^{4} - 1}

\frac{1}{x ^{2} + 1}

Solution steps

\frac{x ^{2} - 1}{x ^{4} - 1}

Factor

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

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

Factor

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

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

Cancel the common factor:

x + 1

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

Cancel the common factor:

x - 1

= \frac{1}{x ^{2} + 1}

(7 y^{6})^{2} (2 y^{8})^{4}

\frac{2 x y - 2 x + 3 - 3 y}{18 x ^{3} + 15 x ^{2} - 63 x}

\frac{( 3 r ) ^{3}}{3 r}

6 x^{2} - 5 x + 3 - (3 x^{2} + 8 x - 4)

6 + \frac{4}{3}