Answer
$ -\frac{1}{x(x+h)} $.
Work Step by Step
The given expression is
$\Rightarrow \left ( \frac{1}{x+h}-\frac{1}{x} \right) \div h$
The LCD of the denominators in the bracket is $x(x+h)$.
Multiply the numerator and denominator
$\Rightarrow \left ( \frac{x}{x(x+h)}-\frac{x+h}{x(x+h)} \right) \div h$
Add numerators in the bracket because both denominators are equal.
$\Rightarrow \left ( \frac{x-(x+h)}{x(x+h)} \right) \div h$
Simplify.
$\Rightarrow \left ( \frac{x-x-h}{x(x+h)} \right) \div h$
$\Rightarrow \left ( \frac{-h}{x(x+h)} \right) \div h$
Invert the divisor and multiply.
$\Rightarrow \left ( \frac{-h}{x(x+h)} \right) \cdot \frac{1}{h} $
Cancel common terms.
$\Rightarrow -\frac{1}{x(x+h)} $.
