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

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

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

simplify

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

a^{2} + a + 1

Solution steps

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

Factor

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

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

1 - a = - (a - 1)

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

Cancel the common factor:

a - 1

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

Apply the fraction rule:

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

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

Apply the fraction rule:

\frac{a}{1} = a

= a^{2} + a + 1

\frac{243}{4}

2^{5} \cdot 3^{- 5}

\frac{2 a ( a + 4 )}{a} - \frac{2 a ( 3 a - 4 )}{2 a}

10 x^{- 2}