Answer
$\displaystyle \frac{3x^{2}-2x+5}{x^{2}-1}$
Work Step by Step
Adding fractions: we need a common denominator:
$(x+1)(x-1)$
$...=\displaystyle \frac{(x-4)(x-1)+(2x+1)(x+1)}{(x+1)(x-1)}$
Numerator, first term, FOIL, second term: FOIL
Denominator : difference of squares
$=\displaystyle \frac{x^{2}-x-4x+4+2x^{2}+2x+x+1}{x^{2}-1}$
Numerator: add like terms
$=\displaystyle \frac{3x^{2}-2x+5}{x^{2}-1}$
