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

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

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

simplify

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

x^{2} + x + 1

Solution steps

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

Factor

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

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

1 - x = - (x - 1)

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

Cancel the common factor:

x - 1

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

Apply the fraction rule:

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

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

Apply the fraction rule:

\frac{a}{1} = a

= x^{2} + x + 1

\frac{3 ( x + 2 ) ( x - 1 )}{6 ( x - 1 ) ^{2}}

\frac{8 x ^{5} y ^{3}}{8 x ^{7} y}

3 a + 5 a

(3 + i)^{2} - (3 - i)^{2}

2 a^{2} + a^{2}