Single Rational Expression 98Fbb7

1. **State the problem:** We need to write $\frac{1}{x} - \frac{1}{x - 2}$ as a single rational expression. 2. **Formula and rules:** To subtract fractions, find a common denominator and combine the numerators. 3. **Find the common denominator:** The denominators are $x$ and $x - 2$, so the common denominator is $$x(x - 2)$$. 4. **Rewrite each fraction with the common denominator:** $$\frac{1}{x} = \frac{x - 2}{x(x - 2)}$$ $$\frac{1}{x - 2} = \frac{x}{x(x - 2)}$$ 5. **Subtract the numerators:** $$\frac{x - 2}{x(x - 2)} - \frac{x}{x(x - 2)} = \frac{(x - 2) - x}{x(x - 2)}$$ 6. **Simplify the numerator:** $$ (x - 2) - x = x - 2 - x = -2 $$ 7. **Final expression:** $$\frac{-2}{x(x - 2)}$$ 8. **Answer:** The single rational expression is $$\frac{-2}{x(x - 2)}$$. This matches the option "-2/[x(x−2)] top-left".