i need help with this?

Question

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

 

(4y²+5y+1)/(y⁴−1)

 

Rational expression in lowest terms: 

 

could someone help please 

Answer 1

(4y²+5y+1)/(y⁴-1)

 

Let's first factor the numerator and the denominator

 

[(4y+1)(y+1)]/(y+1)(y-1)(y²+1)]

 

Notice there's a y+1 factor in both the numerator and denominator.  They cancel one another so we are left with

 

(4y+1)/[(y+1)(y²+1)]

 

which equals

(4y+1)/(y3+y2+y+1)