Answer
$\displaystyle \frac{2x^{2}+9x+1}{x^{2}-1}$
Work Step by Step
... Nothing (no common factors) to reduce...
Numerator:
$(x+4)(2x+1)=$...FOIL...$=2x^{2}+x+8x+4$
$=2x^{2}+9x+1$
denominator:
$(x+1)(x-1)$= difference of squares = $x^{2}-1$
Answer: $\displaystyle \frac{2x^{2}+9x+1}{x^{2}-1}$
