What is (a^3+1)/(a^4-a^3+a-1) ?

The solution to (a^3+1)/(a^4-a^3+a-1) is 1/(a-1)

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simplify (a^3+1)/(a^4-a^3+a-1)

simplify

\frac{a ^{3} + 1}{a ^{4} - a ^{3} + a - 1}

\frac{1}{a - 1}

Solution steps

\frac{a ^{3} + 1}{a ^{4} - a ^{3} + a - 1}

Factor

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

= \frac{( a + 1 ) ( a ^{2} - a + 1 )}{a ^{4} - a ^{3} + a - 1}

Factor

a^{4} - a^{3} + a - 1 : (a - 1) (a + 1) (a^{2} - a + 1)

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

Cancel the common factor:

a + 1

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

Cancel the common factor:

a^{2} - a + 1

= \frac{1}{a - 1}

5 x^{2} - 11 x - 12

\frac{9}{5} + 1

\frac{2 x - 1}{3} - \frac{x + 13}{24} = 3 x + 5 \frac{( x + 1 )}{8}

2 (0 + 1)^{\frac{3}{2}} + C = 1.9

3 (2 x - 1) = (6 x + 5)

What is (a^3+1)/(a^4-a^3+a-1) ?
The solution to (a^3+1)/(a^4-a^3+a-1) is 1/(a-1)