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

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

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simplify (1-x^2)/(x^3-1)

simplify

\frac{1 - x ^{2}}{x ^{3} - 1}

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

Solution steps

\frac{1 - x ^{2}}{x ^{3} - 1}

Factor

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

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

Factor

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

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

(1 + x) (1 - x) = - (1 + x) (x - 1)

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

Cancel the common factor:

x - 1

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

\frac{1}{8} (- 8 c + 16) - \frac{1}{3} (6 + 3 c)

(3 + 1) (3 - 1)

- 2 \times (- 4)

(x + 4 y)^{8}

- 6 + (- 7)