Answer
$\frac{2x+3}{x+2}$
Work Step by Step
We multiply the right fraction by $(1+x)$ to simplify. Then we combine both fractions by forming a common denominator:
$1+\displaystyle \frac{1}{1+\frac{1}{1+x}}=1+\frac{1+x}{(1+x)+1}=1+\frac{x+1}{x+2}=$
$\displaystyle \frac{x+2+x+1}{x+2}=\frac{2x+3}{x+2}$
