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

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

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simplify (ay+a-y-1)/(a^3-1)

simplify

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

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

Solution steps

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

Factor

y a + a - y - 1 : (y + 1) (a - 1)

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

Factor

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

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

Cancel the common factor:

a - 1

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

\frac{13 ! + 12 ! + 11 !}{12 ! + 11 !}

e^{- i \frac{π}{4}}

- \frac{5}{2 ( 1 ^{\frac{3}{2}} )}

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

\frac{a}{a}

What is (ay+a-y-1)/(a^3-1) ?
The solution to (ay+a-y-1)/(a^3-1) is (y+1)/(a^2+a+1)