how to do this math problem?

Question

Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box.

(a−1)/(a⁴ −1)

Answer 1

Hi Jay,

 

 

Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box.

(a−1)/(a⁴ −1)

 

As in another of your questions, you had to factor the difference of perfect squares

a²-b²=(a+b)(a-b)

 

(a⁴ −1)=(a²+1)(a²-1)

 

But since the2nd factor a²-1 is also the difference of perfect squares, it can be factored

a²-1=(a+1)(a-1)

 

 

 

(a−1)/(a4 −1)

 

a-1

-------------

(a²+1)(a²-1)

 

 

a-1
------------------
(a²+1)(a+1)(a-1)

 

 

Now the a-1 factor can be cancelled leaving

 

 

1
-------------
(a²+1)(a+1)

 

 

And that's your answer.