If a is not equal

Question

If a is not equal to -1,0, or 1 then (a(a³+2a²-a-2) + a²-1) / a(a²-1) = ?

Answer 1

(a(a³+2a²-a-2) + a²-1) / a(a²-1) =

 

The cubic expression factors:

 

= [a(a+2)(a²-1) + (a²-1)] / a(a²-1)

 

Now factor the (a²-1) out of the terms in the numerator:

 

= (a²-1)[a(a+2) + 1] / a(a²-1)

 

The (a²-1) terms in the numerator and denominator cancel.  Multiply out the remaining terms in the numerator and combine like terms:

 

= [a² + 2a + 1]/a

 

= (a+1)²/a