1. **State the problem:** Simplify the expression $$\frac{x}{x^{2-1}} - \frac{x-3}{x-1}$$. 2. **Rewrite the powers:** Note that $$x^{2-1} = x^1 = x$$, so the first fraction becomes $$\frac{x}{x}$$. 3. **Simplify the first fraction:** $$\frac{x}{x} = 1$$, assuming $$x \neq 0$$. 4. **Rewrite the expression:** Now the expression is $$1 - \frac{x-3}{x-1}$$. 5. **Find a common denominator:** The common denominator is $$x-1$$, so rewrite 1 as $$\frac{x-1}{x-1}$$. 6. **Combine the fractions:** $$ \frac{x-1}{x-1} - \frac{x-3}{x-1} = \frac{(x-1) - (x-3)}{x-1} $$ 7. **Simplify the numerator:** $$ (x-1) - (x-3) = x - 1 - x + 3 = 2 $$ 8. **Final simplified expression:** $$ \frac{2}{x-1} $$ **Answer:** $$\frac{2}{x-1}$$, with the restriction $$x \neq 0$$ and $$x \neq 1$$ to avoid division by zero.