Simplify the complex fraction $\frac{\frac{1}{x-a} - \frac{1}{a}}{x}$.

1. Problem Description

Simplify the complex fraction $\frac{\frac{1}{x-a} - \frac{1}{a}}{x}$.

2. Solution Steps

To simplify the given complex fraction, we first simplify the numerator. The numerator is $\frac{1}{x-a} - \frac{1}{a}$. To subtract these two fractions, we need to find a common denominator, which is $a(x-a)$.

So, we have

$\frac{1}{x-a} - \frac{1}{a} = \frac{a}{a(x-a)} - \frac{x-a}{a(x-a)} = \frac{a - (x-a)}{a(x-a)} = \frac{a - x + a}{a(x-a)} = \frac{2a - x}{a(x-a)}$.

Now, we can rewrite the complex fraction as

$\frac{\frac{2a - x}{a(x-a)}}{x} = \frac{2a - x}{a(x-a)} \cdot \frac{1}{x} = \frac{2a - x}{ax(x-a)}$.

3. Final Answer

The simplified fraction is $\frac{2a-x}{ax(x-a)}$.