could someone help me with math?

Question

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

 

(2r²+7r+3)/(r⁴−81)

 

Answer 1

Jared,

 

Just like the other problem, factoring is key to simplifying these expressions

 

2r² + 7r+3 = (2r+1)(r+3)

r⁴-81 = (r²+9)(r²-9) = (r²+9)(r+3)(r-3)

 

Substituting these factors into the original expression, we have

 

 

   (2r+1)(r+3)

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

(r²+9)(r+3)(r-3)

 

In this form we see there is an r+3 factor in both the numerator and denominator which cancel one another.  This simplifies to:

 

     2r+1

-------------   = 

(r²+9)(r-3)

 

       2r+1

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

 r³-3r²+9r-27