could someone help me solve this?

Question

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


(r³-8)/(r²-4)

 

 

Answer 1

r³ - 8 is a difference of 2 perfect cubes : r and 2 (2³ = 8)

 

We know that given a³ - b³, it can be factored into : (a-b) * (a² + ab + b²)

 

Therefore, r³ - 8 or r³ - 2³ can be factored into: (r - 2) * (r² + 2r + 4).

 

r² - 4 can be factored down to (r +2) and (r - 2)

 

When plugged back into the problem we get:

 

(r - 2) * (r² + 2r + 4)

__________________

 

     (r +2)*(r - 2)

 

We know that (r-2)/(r-2) = 1 , leaving us with the answer:

 

 r² + 2r + 4

___________

 

    r +2