Answer
$-\frac{1}{x + 1}$
Work Step by Step
1. Find the LCD of all the fractions:
$x + 1$ and $x$ are the denominators, making the LCD $x(x+1)$.
2. Multiply the numerator and denominator by the LCD to clear fractions:
$\frac{\frac{1}{x + 1} - \frac{1}{x}}{\frac{1}{x}} = \frac{\left(\frac{1}{x + 1} - \frac{1}{x}\right) \cdot x \cdot (x + 1)}{\frac{1}{x} \cdot x \cdot (x + 1)}$
3. Distribute:
$\frac{\left(\frac{1}{x + 1} - \frac{1}{x}\right) \cdot x \cdot (x + 1)}{\frac{1}{x} \cdot x \cdot (x + 1)}$ = $\frac{\frac{x (x + 1)}{x + 1} - \frac{x (x + 1)}{x}}{\frac{1}{x} x (x + 1)}$
$=\frac{x - (x + 1)}{x + 1}$
$=-\frac{1}{x + 1}$
