Answer
$ \frac{1}{(x+1)(x+h+1)}$.
Work Step by Step
The given expression is
$\Rightarrow \frac{\frac{x+h}{x+h+1}-\frac{x}{x+1}}{h}$
Multiply the numerator and the denominator by $(x+1)(x+h+1)$.
$\Rightarrow \frac{(x+1)(x+h+1)}{(x+1)(x+h+1)}\cdot \frac{\frac{x+h}{x+h+1}-\frac{x}{x+1}}{h}$
Use the distributive property in the numerator to multiply every term by the LCD.
$\Rightarrow \frac{(x+1)(x+h+1)\cdot\frac{x+h}{x+h+1}-(x+1)(x+h+1)\cdot\frac{x}{x+1}}{(x+1)(x+h+1)\cdot h}$
Simplify.
$\Rightarrow \frac{(x+1)(x+h)-(x+h+1)(x)}{(x+1)(x+h+1)\cdot h}$
Apply FOIL method and the distributive property.
$\Rightarrow \frac{x^2+x+xh+h-x^2-xh-x}{(x+1)(x+h+1)\cdot h}$
Simplify.
$\Rightarrow \frac{h}{(x+1)(x+h+1)\cdot h}$
Cancel common terms.
$\Rightarrow \frac{1}{(x+1)(x+h+1)}$.
