Answer
$\displaystyle \frac{x+2}{x+1}$
Work Step by Step
Numerator:$\displaystyle \qquad \frac{4+x}{(x+1)^{2}}$
Denominator: LCD=$(x+1)(x+2)$
$\displaystyle \frac{3}{x+1}\cdot\frac{x+2}{x+2}-\frac{2}{x+1}\cdot\frac{x+1}{x+2}=\frac{3x+6-(2x+2)}{(x+1)(x+2)}=\frac{x+4}{(x+1)(x+2)}$
Convert Numerator $\div$ Denominator to multiplication
$\displaystyle \frac{4+x}{(x+1)^{2}}\cdot\frac{(x+1)(x+2)}{x+4}$
... cancel common factors, $(x+4),\ (x+1)$
$=\displaystyle \frac{x+2}{x+1}$
