Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises - Page 51: 61

$\frac{x+3}{x+1}$

We multiply the numerator and denominator by $x+2$, then simplify: $\displaystyle \frac{1+\frac{1}{x+2}}{1-\frac{1}{x+2}}=\frac{(x+2)(1+\frac{1}{x+2})}{(x+2)(1-\frac{1}{x+2})}=\frac{(x+2)+1}{(x+2)-1}=\frac{x+3}{x+1}$